# Using the integral test, how do you show whether #sum 1/(n^2+1)# diverges or converges from n=1 to infinity?

##### 1 Answer

May 27, 2015

Before using the integral test, you need to make sure that your function is decreasing, so we get:

and

Which is negative for all

Thus our series is decreasing.

we also need to know that the function is always positive, which we can see that it is.

Then we can solve for

of which we can see that it is

Thus by the integral test, our series is **convergent**