A list of some of absolutely convergent series together.

Question

I have worked on a topic related to the sequence and series. In this way, I need to have some series $\sum_{n=0}^{\infty} a_n$ such that they are absolutely convergent. I studied some books such as the calculus (louis leithold or thomas or rudin ,...).Also I checked some websites on internet.

But now I am looking for " a list of some of absolutely convergent series on a sheet together" (I mean for example some of them recorded on a sheet, such as integral formulas lists, my favorite is they will be special or well-known series or have a closed forms).

I pretty appreciated any help. thanks a lot.

Answer 1

• All geometric series with a common ratio in $(-1,1)$;

• All Riemann zeta series with the exponent $>1$;

• A lot of Taylor expansions, within their radius of convergence ($(1+x)^\alpha, \log(1+x)$, $e^x, \cos x, \sin x\cdots$).