Using the integral test, how do you show whether #sum 1/(n^2+1)# diverges or converges from n=1 to infinity?
Before using the integral test, you need to make sure that your function is decreasing, so we get:
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