# Math Help - alternating series help

1. ## alternating series help

is the following series an alternating series?

Sum n=1, inf, cos(npi)/n^2

can i write it as Sum n=1,inf, ((-1)^(n-1))/n^2, then use the alternating series test, and put it in absoulte value and get 1/n^2 which is a convergent p series? is this correct? thanks

2. Originally Posted by andrewt328
is the following series an alternating series?

Sum n=1, inf, cos(npi)/n^2

can i write it as Sum n=1,inf, ((-1)^(n-1))/n^2, then use the alternating series test, and put it in absoulte value and get 1/n^2 which is a convergent p series? is this correct? thanks
Yes, Sum n=1, inf, cos(npi)/n^2 is an alternating series.

3. and it will converge since its a p-seires, and that means that the original series will converge? thanks

4. Originally Posted by andrewt328
and it will converge since its a p-seires, and that means that the original series will converge? thanks
correct!

5. awsome, thanks for the help!!