Convergence/divergence of series

[sajib_mostofa]

I have a few questions regarding this:

1. When using the comparison test, how do I know which series to compare against? How do I know if the series I chose is converging or diverging?
2. Can anyone give me a rundown of the situations to use the comparison, ratio and integral test?

[TrueTears]

I have a few questions regarding this:

1. When using the comparison test, how do I know which series to compare against? How do I know if the series I chose is converging or diverging?
2. Can anyone give me a rundown of the situations to use the comparison, ratio and integral test?

1. Well it just comes with practise, there's no "set list of series" to compare against, you just have to be smart/wishful thinking and compare to series which you already know that is converging or diverging.

[sajib_mostofa]

I see. Just another quick query:
Say I'm comparing series A to series B. I know that series B is convergent but for the first three values of n, series A > series B. Can I still say series A is convergent or does Series A  have to be less than Series B for all n?

[moekamo]

well the first three terms of a series are irrelevant since they will 'normally' just be integers. So if you compare series for n=3 to infinity, if it diverges, the result of the comparison test will give divergence whether you start at n=3 or n=1, and the same for convergence.

[TrueTears]

I see. Just another quick query:
Say I'm comparing series A to series B. I know that series B is convergent but for the first three values of n, series A > series B. Can I still say series A is convergent or does Series A  have to be less than Series B for all n?

No you can't, not necessarily for all n, but rather for