Monday, 3 March 2014

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 .

No comments:

Post a Comment

Our Latest Post

How to find log (alpha+ i beta), Where alpha and beta are real

Here is the video to show the details of solving this problem. It is an important problem for basic understanding about the logarithm of re...

Popular Post