Calculus 2 Series Convergence Test Review (integral test, direct comparison, limit comparison)
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- เผยแพร่เมื่อ 1 ก.ค. 2024
- Series Convergence Tests Review: the integral test, direct comparison test, and limit comparison test.
Get the file and the notes first: / 102348401
0:00 overall review
6:35 Q1 series of 1/(n(n+2))
17:08 Q2
25:09 Q3
31:56 Q4
36:54 Q5
42:26 Q6 Series of sin(1/n^2)
46:12 Q7
49:52 Q8 Series of 1/(n*sqrt(n))
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#3 isn't hard to understand. Just split the series into 1/(2²*ln2) + (the series starting with n=3). Since the both terms are finite numbers, the sum is also finite.
For Q2 it is very convenient to use integral test
#4 The nth root of x is greater than 1 if n>1 and x>1.
For #1 why did and do we have to plug in zero and the opposite for in the other video we didn’t do that
21:31 I felt that
Hello!! I want to ask you. Why haven’t you ever talked about inverse function for the factorial? I think it would be interesting but I don’t seem to find it anywhere.
cause it doesn't exist
@@akul2986 not even in gamma form?
@@akul2986 I want to know why!! That is why I want The Video.
@@xinpingdonohoe3978 I thought The same. Couldn’t you re organize The gamma function in any meaningful way?
At least for the case of real numbers, the factorial/gamma function should have an inverse for numbers greater than 1.4616... since it's injective from there.
The direct comparison test also works for 6, if you use the fact that 0