Use of Comparison Test
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 vn requires practice .
However if ,
un=P(x)/Q(x), then choose
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 summation of 1/n to power p will act as primary or auxiliary series for testing the convergence of a series by comparison test .