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Sequences, Factorials, and Summation Notation
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- Опубликовано: 8 авг 2024
- You may have this scary looking upper case sigma before. But don't worry, it just means to add some things up! Once we understand how series work, we can do all kinds of other things. Also, have you ever seen numbers with exclamation points after them? No it, doesn't mean that you shout the number. Those are factorials! We will learn about those in here as well. Lots of good stuff in here!
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*He knows about all kinds of stuff... Professor Dave Explains!* Love it.
Well it's "he know A LOT about all kinds of stuff..."
You forgot the "woom" at the end
Yah,but it doesn't mean shit if he can't explain it
@@charliechuma8061 He's got a whole channel explaining it
@@farhanahmed2508i like how you replied to a reply that's been done almost 5 years after you commented.
Your comprehension check at the end uses the word "series," but what you have there are sequences. A sequence is a list. A series results from adding the numbers in the list together.
For factorials, the sequence rule is:
a(n) = n * a(n - 1).
As long as you define a(0) := 1
I was waiting for this video a lot of time. I finally understood what does this sigma means.
9:32 we can add and find sum =-1/12
well explained! helped me a lot!
Would you mind adding this to the calculus playlist??? I was wondering why I hadn't watched this before!
well the introduction to these concepts is taught in algebra, so in the math playlist this happens way before calculus, i figured just linking to it with a card would be enough!
9:31 mathematician ramanujan from India gave the theorem regarding the sum of all the natural numbers upto infinity and that was. -1/12 it can be confusing that how can the sum of natural numbers be a negative fraction but this is the magic of srinivasan Ramanujan. Please don't say after today that numbers till ♾️ can't be added. And thank you for such an amazing video.♥️
Thx for that video. How you see the patterns for series?
this is a very good introduction to analysis at uni
hii, i would like to ask if i can find the sigma notation ‘E’ with using only the series, if that makes sense. for example. (2,4,6,8,10) i have to find the ‘E’ of this series. is there a formula to find a sigma notation with using only the series?
Your explanation of e was really cool! Can you make a really in-depth video about e? I feel like it's everywhere, but still kind of mystifying. The same with ln.
memeingtheoughenglish7221
Tbh, yeah.
I saw it in, like, _one_ class in highschool.
For such an incredible number as it's often touted, doesn't seem to receive proper treatment until softmore undergrad.
Like James Maxwell.
Great video!
Nice vid as always!
no, it's the worst video ever
I love your lessons, thank you, inshallah I'll soon learn physics course too
thanks very much
Thankyou soooooooo much
Very simple Actually ! : )
Lloyd Smith you have the Coolest channel ever !
Professor Dave for the first comprehension question can the answer be :: an-1 +3?
How do we determine the lower limit?
One question. What does i=1(for example) under sigma means???
it means start the summation at i = 1, so you start by plugging in 1 and go from there!
Professor Dave Explains Thanks,professor!!!!! Are you going to make a tutorial about capital pi???
Thank you, sir! You are literally saving my life
when i have the sigam notation i always use i in stead of n is this a problem ?
Thanks
Might I mention how *truthfully **_based_* it is that Dave teaches sequences so early? I didn't these things in college and they feel _largely_ out of place in their conceptual simply being introduced *_after_* limits...
This was so fun to solve.
Totally Awesome Prof. Dave. 🥳 You've made it so easy to understand. 🤩 I'm no longer scared of math! 🥳 The college textbooks don't even compare to what you give us here. 😊 I can finally see myself understanding computer graphics! 🤩 Thank you so much! 🥰🎉👍🏽💻
Pegisus2501
"I'm not longer scared of math"
A blessed sentence if _I've_ seen one!
After some brain mashing, my answer to the second question was "a(n) = (a(n-1) - a(n-2)) + a(n-1) + 4". Seeing the actual answer made me cringe(at myself). Anyways, thanks prof.
yes, i had exactly the same problem. i figured that the numder, by wich the sequence icreases, increases by 4 each time.
So I got a different answer for 1) a1 + 3(n-1) = an
Would that be wrong? It still works but I think I over complicated it.
Thanks for the video. I'm a little confused at 2:20 . How does 2 * 3 to the N power - 1 give us 18 or 54?. Is N the term number?
2 * 3 ^ (1 - 1) = 2 * 3 ^ (0) = 2 * 1 = 2
2 * 3 ^ (2 - 1) = 2 * 3 ^ (1) = 2 * 3 = 6
2 * 3 ^ (3 - 1) = 2 * 3 ^ (2) = 2 * 9 = 18
2 * 3 ^ (4 - 1) = 2 * 3 ^ (3) = 2 * 27 = 54
....and so on...
Yes
Could you do some multivariable calculus?
don't worry i'll get there!
What is the capitalised pi notation? I heard it’s used for summation as well
Capital sigma is for summation, capital pi is for product.
So Π(n) = n×n×n×n×n×n...
en.wikipedia.org/wiki/Product_(mathematics)
@@Vagabond-Cosmique thank you!
6:09 How do you know what a1, a2, ... is equal to if it wasn't specified?
Nobody said a(n)=n
Yeah, it was the only thing I didn't quite understand from this lesson.
This reminds me of the time when I had a good comment
Something is definitely missing..cuz i didn't get it at all.. unlike your previous videos..even the ones on calculus
Done.
My problem is how to write those rational ones in closed form.
Straight away I’m lost. What is a sub n?
the little n in subscript
Can e be expressed like this?
∞
Σ (1/n!)
n=1
I got lost after sequence
my humble respect to Sir Isaac Newton
Came for the flat earth videos, stayed for this.
why the heck does he looks like shakes pear!?
feed me more🤩🤩🤩🤩🤩
Ughhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Sir😂😂😂😂 I can't understand do u all tym make just videos.u know I...think that when tym come I will study this stuff now I HV to see first my maths syllabus maybe so I really not interested in ur vid sorry to say
Please brush up your english
He didn't explain well. Didn't explain much at all just stated facts.
No, I also explained it quite thoroughly. The channel is called Professor Dave Explains. Watch it one more time.
He might be blind. Or dump
2+3(0)2+3(1), 2+3(2)
n=0
2+3n
2,8,18,32
Let's divide by 2
1,4,9,16,25
2n² as n=1 until n
1,2,6,24,120
n!
he knows stuff but not a lot of stuff