Question

How do you determine if the series the converges conditionally, absolutely or diverges given `sum_(n=1)^oo (cos(npi))/n^2`?

Answer 1

See below.

Explanation:

The series

`sum_(k=1)^oo 1/k^2` converges

(Basel problem)
https://en.wikipedia.org/wiki/Basel_problem

so

`sum_(k=1)^oo cos(k pi)/k^2 le sum_(k=1)^oo 1/k^2` converges