I am having flashbacks to what I wore in high school, music, PeeChees and 4 color pens now... totally forgot about these type of equations... and now its all coming back to me.🤯🤯
Your precision with pointing out the animated notes always amazed me-surely there’s some trick to it? Because it’s not just the accuracy that’s too good, that could be fixed in post, but also the consistency and precision!
I wonder if it's like a weatherman set-up where he can see a pre-composited display of himself with the motion graphics and uses a remote in his free hand to time the next piece of information. If not then that's quite amazing.
He uses a clicker (you can see it in his left hand). And it is all projected onto the blackboard (via projector). Whenever he needs to move to the next note, he hits the clicker, and it moves to the next note/animation. That's why it is very precise.
I remember these series-summation stuff way back in my 10th and 11th grade especially pre-calculus classes and It was worth it (for me) Thank you for the math information sir and you've made it easier for such viewers. 💗✨
This looks like one of the easiest topics in calculus, imo, in fact, i struggled to understand implicit differentiation more than i struggled with this
If k was a constant, what would you be indexing over? There are no other variables in the expression. It might have been overly casual notation, but it was pretty clear what was intended.
The integral is typically a short hand of a special case of a summation. You initially learn in Calculus that the definite integral is defined by what's called a Riemann sum, which is the limit of a sum where the partition becomes infinitely small (Δx -> dx).
Integrals are usually for the summation of an infinitesimal number of quantities, like you'd use for finding the area under a curve. These are discrete sums, so integration is unnecessary.
@@mrhtutoring Ah, I see. So then, writing "Σ(5,14) 2k" is effectively just a shorthand for "Σ(1,10) 2(k+4)", if I'm understanding correctly? Would it be meaningful or useful, based on your description, to just be able to specify the upper bounds with the lower simply implied to be 1? Thanks!
Sort of, just with an additional step to account for. You can't just take it out and leave it alone, like you can for sigma notation. If you take out the constant, you have to give it an exponent that depends on the number of times you evaluate the PI notation according to the limits of the product structure. As an example, consider: PI of 2/k, from k=1 to k=4 This product structure is evaluated 4 times according to its limits. Thus, you can pull 2 out in front, and apply an exponent of 4 to it. So it becomes: 2^4 * PI of 1/k from k=1 to k=4 So this ends up evaluating to 16/24, which simplifies to 2/3.
To determine a general formula for a summation, you usually need to evaluate several terms of the sum after each value of the upper limit of the sum. Then you need to look for patterns to generalize it. It usually will have a relation to the integral of the summand, but not be an exact match to it. For instance, in this example, you'll expect n^3 to appear in it, where n is the upper limit because the integral of 2*n^2 dn is 2/3*n^3. It won't necessarily have the same coefficient, but it usually will be a function related to it. Indeed this is the case, if you expand out the general formula, it will be 1/3*n^3 + 1/2*n^2/2 + n/6. Different leading coefficient, but still a cubic relationship.
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He explains it with such ease. He is a great teacher.
I remember learning this in statistics class. Pretty neat
🗿 notation
Wow..Thanks so much I now understand this after 20 yrs
I am having flashbacks to what I wore in high school, music, PeeChees and 4 color pens now... totally forgot about these type of equations... and now its all coming back to me.🤯🤯
Your precision with pointing out the animated notes always amazed me-surely there’s some trick to it? Because it’s not just the accuracy that’s too good, that could be fixed in post, but also the consistency and precision!
I wonder if it's like a weatherman set-up where he can see a pre-composited display of himself with the motion graphics and uses a remote in his free hand to time the next piece of information.
If not then that's quite amazing.
Its projected
He uses a clicker (you can see it in his left hand). And it is all projected onto the blackboard (via projector). Whenever he needs to move to the next note, he hits the clicker, and it moves to the next note/animation. That's why it is very precise.
And I somehow missed that it is a projector and not an animation. Your comment is appreciated @@deaondre
I remember these series-summation stuff way back in my 10th and 11th grade especially pre-calculus classes and It was worth it (for me) Thank you for the math information sir and you've made it easier for such viewers. 💗✨
Very nice. I needed this!
Or there’s the formula after k^2: n(n+1)(2n+1)/6 where n = 5 in this case
5(6)(11)/6 = 5*11 = 55
Then times 2 = 110
Thank you so much 🙏
Fully understood! Amazing!
All clear, Mr
Thank you so much. I really hope this helps on my calculus test.
Best of luck!
You make it seem like everything’s gonna be alright.
My daughter is gonna be spending hours on your channel... 😊
This looks like one of the easiest topics in calculus, imo, in fact, i struggled to understand implicit differentiation more than i struggled with this
SIGMA!!! AKA GREEK -
Excellent!
Very interesting and necessary to know!
Please make a video on the NBT Exemplar South African Entrance exam 🙏🙏
I love the economy of symbols.
Sigma teacher 🗿🗿🗿
neat
🤝❤
I don't like leaving out the index variable.
Let's say it's n = 1 to 5, then k would be a constant and the result would be 2k^2*15.
Good point. I didn't even notice it was missing, which certainly is important
If k was a constant, what would you be indexing over? There are no other variables in the expression. It might have been overly casual notation, but it was pretty clear what was intended.
So sir what is the use of Sigma notation
Great example, do you have something regarding DFT and FFT?
❤
2[n(n+1)(2n+1)/6]where n=5
Thank you for sharing!
My pleasure!
Much better than our Arnab sir
Please do a video on special trigonometry.
Mostly for repetitive addition. Statistics is a compounded variance. Quatized computing.
{Sum(k²) if(k =0 --> n) } =
n(n+1)(2n+1)
----------------------
6
Anks prof.
Thanks.
I used the formula for the sum of squares, S= k(k+1)(2k+1)/6. When multiplied by 2,we get k(k+1)(2k+1)/3. Substitute k= 5 and you will get the answer
Yep, that's the formula for SIGMA N²
Someone actually explained what that weird looking E actually means, hooray.
Chl ab ek plate momos lga 😛😛
What's the difference between this sign and the integral?
The integral is typically a short hand of a special case of a summation. You initially learn in Calculus that the definite integral is defined by what's called a Riemann sum, which is the limit of a sum where the partition becomes infinitely small (Δx -> dx).
Integrals are usually for the summation of an infinitesimal number of quantities, like you'd use for finding the area under a curve. These are discrete sums, so integration is unnecessary.
110k
Did you make this video with 110 as the answer on purpose? Because your subscribers surpassed 110k. Coincidence, right?
Hello sir I am from India . Can you pls make videos on trigonometry of 10 th standard
Nope
Too easy to do yourself
Try to study from Ritik sir (physics wallah) hope it will help. Hare Krishna ❤️
ikr@@ojassaini5547
🗿
can we get same aanwer by integration sir?
This would have been better had he shown the n(n+2) (2n+1) /6 formula.
The formula is n(n+1)(2n+1)/6. The second expression in the parentheses is (n+1), not (n+2).
What if the numbers above and below then Sigma are not integers? Is there a defined process for that, or is my question just dumb?
They have to be integers.
They represent terms of the series, such as 1st, 2nd,3rd...
@@mrhtutoring Ah, I see. So then, writing "Σ(5,14) 2k" is effectively just a shorthand for "Σ(1,10) 2(k+4)", if I'm understanding correctly?
Would it be meaningful or useful, based on your description, to just be able to specify the upper bounds with the lower simply implied to be 1?
Thanks!
Lower bound can be any integer as well.
why is the same letter used for sumatory and variance , ahh my linguistics head can't
what if the 5 is replaced with an n
Can you also take to coefficient out in Pi Notation?
Sort of, just with an additional step to account for. You can't just take it out and leave it alone, like you can for sigma notation. If you take out the constant, you have to give it an exponent that depends on the number of times you evaluate the PI notation according to the limits of the product structure.
As an example, consider:
PI of 2/k, from k=1 to k=4
This product structure is evaluated 4 times according to its limits. Thus, you can pull 2 out in front, and apply an exponent of 4 to it. So it becomes:
2^4 * PI of 1/k from k=1 to k=4
So this ends up evaluating to 16/24, which simplifies to 2/3.
@@carultch Thank you very much
How do u do it when the summation is bigger like for example: we need summation from 1 to 100 of k^2
socratic.org/questions/how-do-you-find-the-sum-of-the-series-k-2-from-k-1-to-35
Here's the formula
To determine a general formula for a summation, you usually need to evaluate several terms of the sum after each value of the upper limit of the sum. Then you need to look for patterns to generalize it.
It usually will have a relation to the integral of the summand, but not be an exact match to it. For instance, in this example, you'll expect n^3 to appear in it, where n is the upper limit because the integral of 2*n^2 dn is 2/3*n^3. It won't necessarily have the same coefficient, but it usually will be a function related to it.
Indeed this is the case, if you expand out the general formula, it will be 1/3*n^3 + 1/2*n^2/2 + n/6. Different leading coefficient, but still a cubic relationship.
Thank you 🙏
Sum of square of first k natural numbers is k(k+1)(2k+1) whole divide by 6.
Enter into Ti-83/TI-84:
sum(seq(2K²,K,1,5))
Why only asian dad can do maths better I wonder 😂😂
Asians🙄
but thank you so much.
Why the eye-roll emoji 💀
This guy is literally Sigma
Knew someone would say this joke