## Ratio Test

### Examples 4.2.16(b):

We have to check the *lim sup* of the expression

Clearly, the

*lim sup*of this expression is equal to 1/2. Hence, by the ratio test the series converges absolutely.

The root test for this series, of course, gives the same result. However, it is much easier to compute the limit of the above expression rather than computing it for the expression resulting in the root test.