# How do you use the ratio test to test the convergence of the series #∑k/(3+k^2) # from k=1 to infinity?

##### 1 Answer

Aug 14, 2018

Let:

and evaluate the ratio:

We have that:

so the ration test is in effect inconclusive to determine whether the series:

is convergent.

However if we consider the harmonic series:

which is divergent and we apply the limit comparison test, we can see that:

so, as the limit is finite, the two series have the same character and we can conclude that;

is divergent.