I have a doubt regaring Series(Convergence & Divergence)

Question

anonymous · Answer

Hi! I might be able to help you. What's your question? :)

dls · Answer

There are so many tests available to test convergent and divergent nature. 
I don't know which one to apply when?

anonymous · Answer

Hmm, that's true, and to be honest I'm not sure I can help you with a general method.

dls · Answer

Like when I see a method IDK which one should I try.

anonymous · Answer

Is there a particular example you were thinking of?
Generally I just take all of the methods that I've been taught, and try them out, one at a time.

anonymous · Answer

With practice, you might be able to jump directly to the correct one straight away.

anonymous · Answer

Were you thinking of any particular question?

dls · Answer

well not atm

anonymous · Answer

Fair enough. Sorry that I can't be of more help!

dls · Answer

haha np!

abb0t · Answer

When in doubt, use $ratio~test$. It generally works for most series problems. If it doesn't work, then try a new series test.

dls · Answer

there are 2 ratio test I guess,
Higher and lower? D alemberts and Rabbes?

ganeshie8 · Answer

So basically you're given a series :
$$\large \sum \limits_{n=1}^{\infty} a_n$$

and you want to know the order of convergence tests to try

ganeshie8 · Answer

1) Always apply `limit test` first :
$$\large \lim \limits_{n\to\infty}a_n \ne 0 \implies  \text{ the series diverges}$$

ganeshie8 · Answer

If limit test is silent, next use any of below tests(no particular oder) 
`root test`
`ratio test`
`limit comparison test`

ganeshie8 · Answer

@Kainui  @ikram002p @dan815   wanna correct/add anything ?

dan815 · Answer

yes :) just do a practice problems of all kids and get some intuition

ganeshie8 · Answer

:) there is no substitute for practice !
there is also `alternating series test` exclusively for alternating series

if  all the above tests are silent, you can always turn to wolfram or take a paper and manually compute the partial sums and analyze how they're behaving

anonymous · Answer

my fav is always comparison test bhahaha

kainui · Answer

Often times I see people get so wrapped up in doing this test or that test that they sorta forget what it is they're literally looking at and it might be completely obvious that it diverges. So step back a bit and just ask yourself realistically what's going on. For example, there might be like a fairly normal looking sum with "sin(n)" thrown in. Ok, well all that's going to do is give you values that are between -1 and 1. So it's usually not going to really affect the convergence of your series if it normally would without the sine.