# Math Help - Does it convert or not?

1. ## Does it convert or not?

This is a row and im supposed to determine if it does convert, or goes against infinity (divergens is the norwegian word for this)

Sum between n=1 and infinity: $((-1)^n*n+1)/n^2$

I really need to do this one before my test

2. The given series is the sum of series:

$(i)\; \displaystyle\sum_{n=1}^{+\infty}\dfrac{(-1)^n}{n}\quad (ii)\;\displaystyle\sum_{n=1}^{+\infty}\dfrac{1}{n ^2}$

The former is an alternating series, use the Leibnitz test to prove that is convergentt. The latter is convergent ( $p$ series with $p>1$ ). The sum of two convergent series is convergent.