Question

Could you please tell me in which cases, what convergence/divergence tests to use? We have to know:
the divergence test
the integral test
direct comparison test
limit comparison test
alternating series test
absolute convergence test
ratio test.

Answer 1

@Neemo @mukushla

Answer 2

if there are factorial use ratio

Answer 3

never use integral because it takes forever

Answer 4

if its rational expression use limit comparison or comparison test

Answer 5

alternating series is used when you see -1 raise to any n power

Answer 6

root test is when there are nth power

Answer 7

divergence test is when you examine the problem and it doesnt look like it approach 0

Answer 8

hmm. so if you have something like:
\[\sum_{n=2}^{\infty}(-1)^n/n((lnn))^101\]

sorry, the last bit is lnn^101

Answer 9

alternating series

Answer 10

because u have -1^n power

Answer 11

series are useless unless your math major

Answer 12

i dont see many applications with it like dervivative and integral

Answer 13

i dunno cuz the mark scheme:
http://www.math.ubc.ca/~gupta/m101_common/M101Final201204_solns.pdf

here for 4. part a.
they used the integral test. and I dunno why. i would've used the alternating series test.

Answer 14

because they didnt answer if series was convergent or divergent

Answer 15

they want to know if it was absolutely or conditionally or divergent

Answer 16

so he used the absolute test

Answer 17

and then used the integral to test for divergence because integral test is easy to apply in this case

Answer 18

if he found the series to be convergent using integral test that means the series is absolute convergent, which mean convergent series as well

Answer 19

if this series just ask for convergence or divergence then alternating series test is the way to go but it didnt