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 .

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