I Wish I Saw This Before Calculus
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- Опубликовано: 1 авг 2024
- This is one of my absolute favorite examples of an infinite sum visualized! Have a great day!
This is most likely from calc 2 (calculus 2) sum n = 1 to infinity 1/2^n
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(1 / 2) ^ n
#math #brithemathguy #shorts
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Bro u wrong(ish). A better answer would be 1-2^(-n) aka 1 minus 2 to the negative power of how many items the sum has. (And ye im not that stupid and i know that if n tends to infinity 2^(-n) tends to 0 but ey, it aint 0 :)
There is a formula for this type of problem...( first term)/1-multipler
That was the cleanest loop I have ever seen
I would’ve thought it was 0.99 recurring, as logically that space should never be filled.
Almost 1 😂
That’s the smoothest loop I’ve seen so far.
Clean 💯
Yeah yeah
Very easily done
Yeah I would say so too
I didn't even realized it was a loop till i saw this comment
this is how old mathematicians form ancient times used to do maths
And this is how we would do it now:
The series is 1/2 + 1/4 +1/8 ...
The pattern for this series:
(1/2) + (1/2 × 1/2) + (1/2 × 1/2 × 1/2)... and so on.
In terms of equation we can write this series as:
x = 1/2 + x/2
Solving this equation we get:
2x = 1+x
x = 1
And that's your final answer
@@adityasingh3963 Actually you would just instantly see it's a geometric series and use the 1/(1-q) thing.
@@aadityaranjan2159 I haven't learnt GP yet so I solved it with simple linear equation.
@@aadityaranjan2159 That's not a creative answer tho. You just used the formula that you were taught in school and didn't come with the solution yourself. You just substituted the values in the formula.
@@adityasingh3963 should i derive the formula for you?
an infinite amount of mathematicians walk into a bar, 1st orders 1 beer, next orders 1/2 beer, 3rd orders 1/4 beer, barman pours 2 beers and says "guys, you should know your limits"
Underrated LMAO
It's it n=0→∞, not if n=1→∞, but still good enough
@@_SweetLittleAngel_no, the problem would still work since he said 2 beers
@@youssefbencheikh8637 Without 1/(2^0) it would be just 1
@@_SweetLittleAngel_ I think he's referring to how the joke still holds true. As it is not referring to the typical limit of 1/2^n but 1/2^(n-1)
“We dont need any calculus”
Immediately takes a limit
It's described calculus without going into calculus. It's Xeno's paradox, philosophically, and on paper, there is always a smaller fraction, but in practice, you can not split a drop of beer in half any further nor take a step small enough to not cross the finish line.
more like a inf geometric series
@@cookiemainsAny infinite series needs a limit. You can't add an infinite amount of things, but you can see what the sum approaches with limits.
@@Daniel31216 thats not calculus then
@@cookiemains How's that not calculus? Series and limits are an essential part of calculus.
Using squares to represent math is basically how it was always done thousands of years ago xD
This is the oldest math trick in the book and is still very usefull ;)
@@a54e how is this more then slightly funny
yet not being taught on schools
@@a54e you can now get out
Now we plug numbers into equations
That is so cool
Technically it never gets to 1, just keeps getting infinitely closer.
Ya so shouldn’t it be 0.99...?
🤣🤣🤣🤣🤣🤣
Yes but 0.999... = 1
Edit : Okay, that's starting to be really annoying to receive thirty messages about "1 =/= 0.999..." without arguments. I think I understood the message so now, please, don't lose your time, replying me, with or without explanations. Thank you.
You could answer it with the interval 1[
As in infinetly close to 1
@@zeptyray no
I was confused when he asked the exact same question when I noticed it looped 😂
Yes, and the irony is... the loop completes the square, the square eliminates the spiral, the spiral collapses to the decimal point (dot), the decimal point (dot) corosponds to the brain, and the brain liberates....
THE THOUGHT. ❤
that loop is so smooth omg
*intense coughing* i can't react or else im gonna cough so much
Best looped video I’ve come across on RUclips so far
yeah, i didnt notice it until i heard "so maybe its infinity?"
Perfectly timed
fax
Very small problem , not a big deal
Come India you will know what's real highschool maths of jee
"it never gets equal to one it just keeps getting closer to it" have you guys ever heard of something called limits? infinitely close to 1 and equal to 1 are the same thing
let, s = 1/2 + 1/4 + 1/8 +...........
s = 1/2(1 + 1/2 + 1/4 + 1/8.......)
s = 1/2(1 + s)
2s = 1 + s
s = 1 (Ans.)
What is epsilon?
@@BabaBabelOm Permittivity of Space is denoted by epsilon (physics-related term)
In terms of mathematics, it's used to show that an element "belongs to" a set (though it's not the epsilon symbol to be precise, it looks something like this --> €)
@@rudranshjoshi2861 Epsilon is also a symbol for an arbitrarily small number or a constant
@@cracknblast8247 Oh I see, gotcha, Thanks for the info mate :)
*A perfect loop doesn't exis-*
?
?
@@Animation_neoit's a joke pn the fact that it is actually a perfecr loop
@@jolanmoussier9267 ?
Another method which does not involve calculus at all:
let this sum be x ,if you multiply the entire sum by 2 you get 1+1/2+1/4+1/8...and so on ,notice how this simply equals 1+x(the original sum) giving us the equation 2x=x+1
therefore x=1
see at the same time your trying to algebra a calculus problem which rlly just cant be a trusted way to solve it, don’t get me wrong I do know this solution is true but algebra doesn’t do well with infinite series
@@funishawsomish5371Plugging the formula of a geometric progression solves this in seconds without calculus
@@funishawsomish5371 Algebra actually works really well with infinite series! Especially in the context of replacing series with variables like x. However it is true that there are cases where algebra can end up giving you a solution despite no solution being possible
Its limits and series and sequences NOT algebra, they are topics in Calculus and Analytical math. Algebraic manipulation is the operation used to get the problem into an identifiable Calculus form. YOU can solve any Calculus problem using many methods it just may become impossibly hard so we use the most convenient tools at hand. Its like saying we don't trust addition and subtraction to solve algebraic equations. Ridiculous assertion! @@funishawsomish5371
@@staticchimera44you get to proove that the series does converge first
“we don’t need any calculus” *visually takes the limit*
Ikr I gave same example to friend when I taught him limits concept
The limit would be 0 for 1/2^n though. Which is actually called the divergence test. If the sequence does not approach 0, it will diverge. Otherwise, the test is inconclusive. The series shown in this video is a geometric series: (1/2)^n where a = 1/2 and r = 1/2. Thus since |r| < 1 this series converges at (1/2)/(1-(1/2))
@@Shiva-ur3ow and of course 1/2 / 1/2 is 1
@@gavintantleff yep
@@Cowmilker98 the limit of the function as n approaches infinity of 1/2^n is 0, but the limit of the summation is different because you are adding each subsequent answer up to infinity so it would be as pictured.
Ok that was the best loop I’ve ever seem
I can tell that it is supposed to loop, but it cuts off too early. For me it says "So now what if I ask you the que-"
Does it finish the whole sentence for you?
@@eamonburns9597 yes it does
@@SamSpeedCubes Interesting
the visual proof is nice, but the loop is impeccable
It is in Geometric progression and to find S ♾️( sum of infinity)
Formula is first term/1- common ratio
By putting value= ½/1-½
= 1
Bro I never get stuck in loops, this is the first one and it freaked me out
Me neither,
Until I saw this,
And thought to myself:
Me neither,
@@ISawSomethingOnTheInternet 🤯
.999 repeating never gets to 1
If the operation is infinite, the answer is alway infinity. Your operation is never finished!! Definition of infinity!!!
@@DarrylAJones but isn't infinity greater than 2?
Me who knows geometric progression:
*Laughs in solving problem in 10 sec*
Hehe yesss
10 sec is too much ....3 sec is sufficient
Same
What you took the nth term?
@@koliheroyash6776 there are infinite terms
Holy crap, that loop is seamless. I applaud your editing, good sir 👍
the voice crack 💀💀
"So NOW what if I ask you the answer?" Have I had my coffee yet?
Lmao 😂
safe play ;)
69 likes. Lmfao
It's one
Let s equal to this serious
Multiply by 2 , minus 1 , solve for s
I am 15 years old 😉
@@user-ry6cz3vs6g I watched your weird video
Bro, that transition was so smooth.
Holy shit I watched it twice without even realizing 🤣
Never even noticed the loop. Great work man.
These comments remind me of this joke: A mathematician and an engineer enter a room with an amazingly attractive person on the other side… they are told they can walk exactly half the distance between them and the person after every 2 minutes. The mathematician immediately storms off complaining that they’ll never meet but the engineer says “eh, within an hour I’ll be close enough for all practical purposes” 😂
An infinite number of mathematicians walks into a bar. The first one asks for 1/2 a beer. The second one asks for 1/4 a beer. The third one asks for 1/8 a beer, and every mathematician asks for half of what the previous one did. The bartender hands over one beer and says, “You’ve ought to learn your limits.”
Edit: Didn’t expect that many likes thx
*Sigh*
That was, not horrible
Learn your limits.. lol, good one. 👍
Can someone tell me if this joke is original(I've never heard it), because this deserves more attention if it is.
@@zizzors9314 No, just retelling
Ahhhh…I saw what you did! Clever…L'Hôpital's rule.
we took a subject named "infinite geometric series" in highschool, which is the way i used to get the answer, 1/2 divided by 1-1/2
Yes me too... In GP series
Yeah, since all the terms are just 1 times (1/2) to the n, we can calculate it as 1/(1-r), where r is the term we're scaling, 1/2 in this case. It'll give us 2 but just subtract the first one ((1/2)^0) and we get that 1/2 + 1/4 + 1/8 ... Equals 1
@@cl0p38 nice!!!
Yes special case of geometric progression!
You took a whole class over that? We went over that in algebra 2 for like a week
everybody gangsta till it doesnt make a full square
Was so smooth loop between ending and beginning that i ended up watching 2 times 😊.
Scumbag move
"we dont need calculus to solve this"
oh yeah we need infinite geometric series, pretty easy.
well its not calculus
@@timmytom2398 it's calculus
@@HaruTch4303 it’s basically an Asymptote where it will never reach 1 but it will forever grow closer and closer to 1
@@bibedexpert65 yep, but since infinity is involved, then it actually will reach 1
it's just that in a real-world context, it wouldn't be possible since infinity isn't a real-world concept
@@HaruTch4303 it’s not
this is the best loop i have ever seen
Let's say, x = 1/2+1/4+1/8+1/16...
Now multiply 2 on both sides we get,
2x = 1+ 1/2+1/4+1/8+1/16...
2x = 1 + x ( x = 1/2+1/4+1/8+1/16...)
2x-x = 1
x = 1
🙂
oooh nice
Ur wrong its 7/8
X never makes it to 1 it only approaches 1.
@@slo526its not just the 3 fractions silly it goes on forever
@@mojaveclimberinfinite sums like these that converge to some x are defined to EQUAL that x
Yooooo usually I don’t fall for looped videos but this one got me
This is exactly the kinda thing I think about when I’m bored, video feels like it was taken directly out of my brain
Maybe you should study math
The loop was so smooth that an still watching the video 😭
An explanation that gives a clear concept.
that loop was so clean, I didn't realize it had started over...
Whats YOUR favorite visual example?
Sum of n first squares
1 = 1/2 + 1/2
= 1/2 + 1/4 + 1/4
= 1/2 + 1/4 + 1/8 + 1/8
= 1/2 + 1/4 + 1/8 + 1/16 +1/16
= 1/2 + 1/4 + 1/8 + 1/16 +1/32 +1/32
= ...etc
The brachistochrone
The general *geometric series proof. It's basically like a crane-looking graph, where 2 lines meet, and that's the answer
1+1/2+1/3+1/4+/5.....1/n
Write it's Sum in Terms of n!
GOD DAMN THAT TRANSITION
Smoove. Flashback to rookie calculus
Great loop!
Glad you think so!
Geometric series, or " The Unveiled story of Achilles and the Turtle" 😍
AGP 🤔
I currently studying GP in my coaching and we did solve this problem just yesterday
@@Anonymous-8080 same except we did it last Saturday
Infinite geometric series with n = 0
It's a geometric progression and the formula for the infinity sum is S= a1/1-q , with 0
Im waiting the moment youre gonna descover that this formula is deducted using limits, hence calculus.
Remember a1 (q^n-1)/q-1 ?
When u put n to infinity, this is calculus, so dont be dumb
THE LOOP IS SO GOOOOOOD
Not as visual as rectangles, but I was familar with binary numbers early in my life (being a computer enthusiast meant learnig assembler in the Eightys) and the limes was immediately clear to me. 1/2 + 1/4 + 1/8 + 1/16 … is 0.1111… in binary, which is 1 for the same reason, 0.9999… in decimal is 1.
That's cool
That's a cool way to see it
SUPER COOL
Wow man I feel enlighted
let, s = 1/2 + 1/4 + 1/8 +...........
s = 1/2(1 + 1/2 + 1/4 + 1/8.......)
s = 1/2(1 + s)
2s = 1 + s
s = 1 (Ans.)
I’ve seen many comments but I am still confused why this can’t be solved algebraically. x= 2^-1 + 2^-2 + 2^-3 …, multiply both sides by two to get 2x= 2^0 + 2^ -1 + 2^-2 + 2^-3… which is equivalent to 2x = 1+ x so x= 1. This seems much more intuitive and simple than limits or infinitely smaller squares.
i mean, that's a really cool method
Oh cool, I really like that!
Beautiful loop. Beautiful math. Good job.
Or just multiply the series (let’s call it: ”x”), by 1/2, to get: (1/2)x = 1/4 + 1/8 + 1/16 + …. Then, align identical terms and subtract (1/2)x from x: x - (1/2)x = 1/2x = (1/2 - 0) + (1/4 - 1/4) + (1/8 - 1/8) + … = 1/2 + 0 + 0 + 0 + … = 1/2. Multiply both sides by 2, for: x = 1. No calculus needed; and you, also, avoid the possibility of x = 1 - ε.
That's so incredible to help us understand!
This loop is godlike. Nice
Dude, it's been 2 days and 5 hours and I am starting to think that this is a loop!
I like how he is teaching this I'm learning.
Omg that was a good loop
Anyone else pause the video and was like it’s 7/8….then heard the rest of the question and went silent?
This guy
no because I didn’t ignore the “+ …”
@@thedeviousduck8027 thanks for adding that in
Guess that’s why limits are a thing
Answer should be limit of 1
I believe the answer will always be
Excellent! Thank you!
first time I saw this is when I discovered that I want to dedicate my life to this
Another method is this: X=1/2+1/4+1/8+...
2X=1+1/2+1/4+...
2X-X=1
X=1
1/2+1/4+1/8+...=1
you would need to figure out x=1 to know 2x = 1 plus the thing
@@thegoldengood4725 you wouldn't. X was defined to be 1/2+1/4+1/8+..., so 2X=2(1/2+1/4+1/8+...)=1+(1/2+1/4+1/8+...)=1+X is actually a pretty intuitive and trivial observation
@@dorian4387 how do u know 2 times the thing is 1 plus the thing
@@thegoldengood4725 2*x = 2*(1/2) + 2*(1/4) + ...
@@thegoldengood4725 ok do you know elementary mathematics mate? Because it’s all basic multiplication xD that 1/2 term in the bracket over there, that times 2 is 2/2 which is 1, and the rest follows. Because this is an infinite sum, they are equivalent from that point
You had me infinitely listening to your clever loop…..
Nice visual proof
Sum(1/n^k) = 1/(n-1) when k is from 1 to infinite
I like to visualize this problem as eating half of a noodle, then taking more bites, every one half as big as the other. The noodle is just halving, and you will never take the final bite.
I get your point but strictly with a noodle we can probably agree on a particular molecular structure that we agree as the smallest possible part of a noodle and when you consider those standardized increments your halfing process would eventually be required to destroy the last unit of noodle.
But even still if you wanna think oh he left an atom behind of the last noodle unit did he really eat the whole noodle?
Do we ever…. ???
@@visibletoallusersonyoutube5928 Nah, you eat that half an atom and explode with the rest of us!
@@DBlueDogGaming I guess it’s a morality question in regards to eating it lol.
That loop was seamless, and the maths was explained very well. Good job!
I totally got stuck in the loop! Omg!!! That was scary.
We can show the sum is 1 in another way.
Take a whole pumpkin. Cut in two halves put a half aside. Cut the another half into two quarters. Put a quarter piece aside and cut another quarter piece.
If we proceed in this manner, we get infinite series same as the question by collecting the pieces kept aside. Now if we merge the pieces one by one those pieces completes one whole pumpkin. So, the sum is 1.
That makes more sense to me.
"I wish I saw this before calculus" bro you MADE the video
Yeah he made the video... About a concept that has existed for ages...
@@blueberrychronic
The format "I wish I’d seen x video before y event" denotes a speaker expressing regret in regards to the fact that they did not, for one reason or another, view x video before y event although it was up for viewership *at the time.*
Is English your first language?
For those who want to do the math: You can use the formula for a convergent geometric formula that is a1/(1-r), the first number (0.5) of the series divided by 1 - the common ratio (also 0.5 because 0.25/0.5 = 0.5), which is equal to 1
cant you just see it’s geometric then do a/(1-r)?
@@musicaltaco6803 This is literally what I have wrote
@@PootisSaver you’re right, sorry! you just actually punched it in and so it was long so i thought you did something else:)
Very nice sir thanks ❤
What a coincidence! I just learned that today at school
Another example that Google is spying on us.
The loop is good... lol
It's in GP (infinite series ) 🙌🏻
Beautiful explanation
Best loop so far
This is a bruh moment.
ruclips.net/video/UndWFyXz_jE/видео.html
This is the best loop I’ve seen
Super easy explanation, thank you so much 😀❤️
Forward progression in this series gets you infitesimally close to one but as x approaches 1 from the right y approaches the local maximum of one. However when x approaches zero, y approaches positive infinity.
Its infinite GP series , so I calculated it in 2 seconds XD
Me too
a/1-r
@@RohanDhandr8 yep
Me too
Same
This can be slove through infinite G.P concept.[a/1-r]
Where 'a' is first term and 'r' is commom ratio.
Solve it 🙂
Thats what i did lol
@@Chan-og3yk 🙃
Wow this is a good way of teaching math I will try to remember this when I am learning claculus
Actually we can also do it by the summation of Geometric Progression in which the numbers are decreasing.
lmao this loop is so smooth, it even ends with a loop(infinity)
I confused this and something else on my Google interview and failed :(
L
Thanks bro😊
This is just a question related to a sum of infinite GP
Loop was so smooth that I didn't notice till a couple of seconds passed after the second time.
This is an exponential function and on a graph it’s line quickly goes towards the x axis aka the one but never touches it so it’s infinitely less than one
Not really the x axis, but the line y=1
Well "infinitely less then one" means it's one. There exists no number that's infinitely close to a number but not the number itself.
Laughs in geometric sum to infinity
that transition was so smooth that i unknowingly watched this like 3 times
Woah that’s actually amazing! I’m not in calculus yet but I’m in geometry and next year I can take two classes probably algebra 2 and precalc
If you love math then you’ll love Calc I’m taking it right now
Advice for if you take advanced math courses in the future: learn your fractions, it has helped me a lot and it makes calculations a lot easier. For example recognize that 0.333... is 1/3 or 0.1666... (when using a calculator it would round to 0.1667) is 1/6 or 0.125 is 1/8 and so on. Really the more you know the better. It helps shorten your expressions and makes problems like 0.75/0.1666...=4.5=9/2 a whole lot easier to do in your head. Keep up the attitude and you'll enjoy using calculus to solve problems like the one in the video.
Don't take Algebra 2 and precalc at the same time. You can do it one semester after the other, but the 2 materials over lap and if you don't learn one, you won't get the other.
Too bad you already are in geometry, because it is possible to take geometry and Algebra 2 at the same time. None of the courses really overlaps much, except for one small unit in Algebra 2.
But later if you want to double math, you can do ap stats with calc, and linear Algebra with multivariable calc if you get to it in high school. Pre calc is basically feeding off of Algebra 2. My class had a test of Algebra 2 information before it started, so it would be near impossible to pass if you haven't taken the class unless you reviewed or learned it yourself outside of school, and/or get tutoring outside of school.
Please don't overwhelm your schedule like that. It's not the brightest idea. I took Algebra 2 and geometry together and graduated high school after taking multi variably calc and linear Algebra. Even if you don't take both at the same time, if you are an 8th grader right now, you can get to AP calculus BC if you try hard enough.
Just a word of advice, if you really do want to take both at the same time, all I have to say is good luck.
@@zurcyro I’ll keep that in mind thx
Another rthing is if you really want to, just learn the Algebra 2 trigonometry over the summer, and the basics of the units in Algebra 2. Then you probably can. Especially the graphing ones in pre calc, it would just be way more work than needed. If you know you can do it, go ahead and try.
It's better to take a class and have an A than to take a harder class/ take more classes and get a B. GPA is more important than the level of class, unless you know you can get an A. Colleges look for self value and knowing self worth. Take care of it.
stopping at any point would make the top number one less than the denominator, so wouldn’t it be (infinity-1) / (infinity)
or am i wrong?
Your logic is correct but there is no fraction that can represent a quantity like this. Infinity can't be quantified so your idea should look something like this 1-(2^(-999...9) which does not equal 1. The thing about infinity is that it is very weird. If you have infinity - infinity it can be equal to anywhere between negative infinity and positive infinity depending on how each infinity is defined. It could equal 0 or 15 billion. It's not easy to explain but infinity-1 is not always a larger number than infinity. So yes you are almost right. Hope this helps :)
You're describing lim x-> inf of (x-1)/x in calculus, which is equal to 1
first well looped video i've ever seen!
That loop is insane
This is literally how I remember that 1/x^2 converges and 1/x diverges. Probably saved me quite a few points on calc exams :D (the sums of them that is)
woah, careful there. 1/x^2 would be 1/4 + 1/9 + 1/16 + 1/25 + ...; This is 1/2^x. (the sum of 1/x^2 still converges though but for a different reason - refer to the 3b1b video for example)
@@decare696 the basel problem eh?
@@decare696 Hey man whatever works XD
Please explain
How can it be 1? I mean it will never reach 1, there will always be a small hole in the square, not matter how many times we repeat this.
With the Infinite concept
We can assume eventually it will reach 1
How
@@puppy-say-moomoo2774 because infinity is never stopping so it will in theory fill in the hole
You’ll never reach 1. You’ll reach a result that’s infinitely close and you’ll get infinite digits after the decimal, but there’ll always be the next fraction missing.
You can approximate to 1 of course, but it’s not the exact result.
@@imdeaf81 if you repeat this infinite amount of times you *will* reach one
loops so clean i can't get out of it
Very interesting and yet simple. Wish my maths teachers were like you instead of just obsessing over grades and assignments.
In theory the value should never reach the number one it'll just get very close, so I wrote a python script to find the value of Y with very large X values, but the problem is that my PC started to round the numbers after they got so complex resulting in a positive outcome, meaning that it starts going up because it rounded it after 60 intergers in the decimal place. So in theory if we could measure numbers more precisely indefinitely than the answer should be jusr slightly below one
Assume, you have a cake. You cut it in half and take away one of the halves. Then you cut the remaining half into two again and take away one of the pieces and go on. So, how many cakes do you slice up?
Thank you for this.
解釋地太好了！