# How do you determine the convergence or divergence of #sum_(n=1)^(oo) cosnpi#?

##### 1 Answer

Feb 7, 2017

The series:

is indeterminate

#### Explanation:

A necessary condition for a series to be convergent is that the sequence of its terms is infinitesimal, that is

We have:

so the series is not convergent.

If we look at the partial sums we have:

#s_1 = -1#

#s_2 = -1+1=0#

#s_3 = 0-1=-1#

#...#

Clearly the partial sums oscillate, with all the sums of even order equal to zero and all the sums of odd order equal to

Thus, there is no limit for