A series is defined by the equations and .

Find the convergence of the series by Ratio test. \ \

Ratio Test : \ \

(i) If , then the series is  is absolutely convergent.

(ii) If  or , then the series is  is divergent.

(iii) If , then the ratio test is inconclusive.

Find .

Squeeze theorem:

Let and be functions such that for all , , Also suppose that then for any , .

Here , then

.

Thus by Squeeze theorem .

.

Series is convergent by Ratio test. \ \

\ \

Series is convergent by Ratio test.