The test is applicable for series of positive numbers only .

For given series

**summation of un***of positive terms,*

a series

**summation of vn***of positive terms*

is to be selected whose convergence is known and

**lim n--> infinty un/vn***is non zero finite number .*

The efficiency is choosing

summation of

**v***requires practice .*

**n**However if ,

**u**

**n***, then choose*

**=P(x)/Q(x)**

**vn=term containing highest power of x in P(x)/term containing highest power of x in Q(x)**which will be finally of the form

**1/n to power p .**Thus

*will act as primary or auxiliary series for testing the convergence of a series by comparison test .*

**summation of 1/n to power p**