does this series converge, and if so is it absolutely convergent?

Question

the series from n=1 to infinity of
((-1)^*n+1))/n^4

I found that by the ratio test it was inconclusive, so no abs. conv
is this right? and how do i know if it is simply convergent?

Answer 1

Is ((-1)^*n+1)) supposed to mean
[(-1)^(n+1)] ?

If so, an infinite series of positive 1/n^4 terms is convergent, based on the integral test. A similar series with alternating + or - terms of the same magnitude must therefore also converge.