Question

Question below

Answer 1

Assume
\[\sum_{n=1}^{\infty} |a _{n}|\] converges. Prove \[\sum_{n=1}^{\infty}(a _{n}+|a _{n}|)\] converges

Answer 2

Also assume you cant use absolute convergence theorem

Answer 3

show that the first term of that sum in that series converges.

Answer 4

you mean the partial sum?

Answer 5

no .. show that if the series converges absolutely, then it's conditionally convergent