# How do you use the convergence tests, determine whether the given series converges #sum (7-sin(n^2))/n^2+1# from n to infinity?

##### 2 Answers

May 23, 2015

If the general term is with the

The function sinus has a range

So:

Since the function

May 23, 2015

First do the limit test for convergence, and check the limit, as the limit needs to equal 0 for a series to be *considered convergent*, if the limit is not 0, it is then divergent.

Thus:

Therefore we can conclude that the series does **not** converge, and therefore is **Divergent**.