# How do you use the limit comparison test for #sum 1 / (n + sqrt(n))# for n=1 to #n=oo#?

##### 2 Answers

#### Explanation:

Since this series is a sum of positive numbers, we need to find either a convergent series

We remark the following:

For

Therefore

So

Since it is well known that

Now using the comparison test, we see that

The limit comparison test takes two series,

If

We should let

Note that

So, we see that

Since the limit is