8:11 I did not understand that part. How can you just subtract both n and k with 9 to get the same value of the sum? Changing k=10 to k=1 and then change k-9 to k do not change the value of the sum. You know that the smallest number of k-9 is 1, since k=10. And as k changes with 1, k-9 will also change by 1. So when k=10, then k-9=1. k=11 then k-9=2. k=12 then k-9=3. You can see that k-9 will be 1, then 2, then 3, then 4 and so on. We can see that k-9 is like another k where it starts as k=1, then k=2 and so on. This k would start with 1. So yes, you can start with k=1 instead of k=10 and use k instead of k-9. So this does not change the sum. So would not changing n+9 to n change the sum? (Sorry for my bad English, if it is bad)
If n were finite, that would be true. But infinity + 9 is the same thing as infinity, and remember we are taking the limit as n approaches infinity. I realise this comment is quite old, but maybe this'll be useful for anyone experiencing the same confusion.
@@maxguichard4337 I don't know why I got a notification when you posted this reply, as this comment is indeed old and I do not at all remember writing this comment nor watching this video. Therefore, I can't really get much value from your comment, but I guess it's still really nice that you spent some of your time trying to help, and as you said, maybe this will be helpful for others 😀👍
Our prof had taught a good method to convert sigma to integration S-1: take one (1/n) out of sigma and inside sigma club all k(ie summation variable) and n in form on (k/n) S-2 Replace 1/n by dx Replace k/n by x Replace sigma by integration snake Lower limit of integration = lim as n tends to infinity (lower limit of sigma ÷ n) Upper limit of integration : lim n tends to infinity (upper limit of sigma ÷ n)
GRE stands for graduate records examination (or something like that). The GRE Math subject test is for people applying to mathematics graduate programs or related areas. It covers all of calculus, and then all the majorsubjects covered in undergraduate mathematics ( a bit of stats, probability, analysis, abstract algebra, lin alg, etc) Heres a practice test if you want to see what its like. www.ets.org/s/gre/pdf/practice_book_math.pdf
You left out the 1over n term at the end of the video when you integrate arcsin..n is not a constant so you have to take it into account when you integrate it..please correct this..
Excellent insight for an incredible solution! Math is an art.
What program do you use to be able to write on a big white board?
Very late but he uses smoothdraw3
you are genius thanks for all these videos
8:11 I did not understand that part. How can you just subtract both n and k with 9 to get the same value of the sum? Changing k=10 to k=1 and then change k-9 to k do not change the value of the sum. You know that the smallest number of k-9 is 1, since k=10. And as k changes with 1, k-9 will also change by 1. So when k=10, then k-9=1. k=11 then k-9=2. k=12 then k-9=3. You can see that k-9 will be 1, then 2, then 3, then 4 and so on. We can see that k-9 is like another k where it starts as k=1, then k=2 and so on. This k would start with 1. So yes, you can start with k=1 instead of k=10 and use k instead of k-9. So this does not change the sum. So would not changing n+9 to n change the sum?
(Sorry for my bad English, if it is bad)
If n were finite, that would be true. But infinity + 9 is the same thing as infinity, and remember we are taking the limit as n approaches infinity. I realise this comment is quite old, but maybe this'll be useful for anyone experiencing the same confusion.
@@maxguichard4337 I don't know why I got a notification when you posted this reply, as this comment is indeed old and I do not at all remember writing this comment nor watching this video. Therefore, I can't really get much value from your comment, but I guess it's still really nice that you spent some of your time trying to help, and as you said, maybe this will be helpful for others 😀👍
Tried to move the whiteboard with finger, but it did not work.
Is the *n*th weekly challenge usually uploaded on the same day as the *(n-1)*th solution video?
Yes, the solution for the last week's challenge and the question for this week's challenge should be posted on the same day. =)
This channel is so good its integrals go up to 11!
You are awesome 💯
Our prof had taught a good method to convert sigma to integration
S-1: take one (1/n) out of sigma and inside sigma club all k(ie summation variable) and n in form on (k/n)
S-2 Replace 1/n by dx
Replace k/n by x
Replace sigma by integration snake
Lower limit of integration = lim as n tends to infinity (lower limit of sigma ÷ n)
Upper limit of integration : lim n tends to infinity (upper limit of sigma ÷ n)
Quick question: Is the author of this video the same guy as the youtube channel blackpenredpen?
I don't think so. They have different voices and accents.
No this individual sounds swedish.
No,of course !!
Its one of his friends that sometimes apears as guest.
Yeah. They both asian
Thanks sir.
Yes I did it
Awesome. This is exactly the kind of stuff I need for GRE math study.
Kyle Bradach what's GRE math study?
GRE stands for graduate records examination (or something like that). The GRE Math subject test is for people applying to mathematics graduate programs or related areas. It covers all of calculus, and then all the majorsubjects covered in undergraduate mathematics ( a bit of stats, probability, analysis, abstract algebra, lin alg, etc)
Heres a practice test if you want to see what its like.
www.ets.org/s/gre/pdf/practice_book_math.pdf
Kyle Bradach thank you. this definitely seems interesting.
Kyle Bradach At what age do people do this?
Well its for grad school. So one would have to finish their bachelor degree first. Anywhere from age 20 and up essentially. Im 25.
Why don't we need to convert the second summation from
k = 0 to n - 1
into
k = 1 to n?
Both works, but second summation is not defined at k=n
Wait, I didn't get how you went from the limits in the summation into the limits in the integration
You left out the 1over n term at the end of the video when you integrate arcsin..n is not a constant so you have to take it into account when you integrate it..please correct this..
It is a Reimann sum, 1/n is the dx term
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Maha tappa question
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