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: $\displaystyle ((-1)^n*n+1)/n^2$

I really need to do this one before my test

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- Mar 3rd 2011, 01:00 AMkaltedetenDagdaDoes 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: $\displaystyle ((-1)^n*n+1)/n^2$

I really need to do this one before my test - Mar 3rd 2011, 01:17 AMFernandoRevilla
The given series is the sum of series:

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

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