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if 0ak1kfor every positive integer k, then the series k=1akconverges. The objective is to whether determine the statement is true or false

Short Answer

Expert verified

false

Step by step solution

01

To determine whether given statement is true or false 

To determine whether the given statement is true or not by using comparison test

02

According to comparison test

k=1akand k=1bkare two series with positive terms such that 0akbkfor every positive integer k

If k=1bkconverges then the series k=1akalso converges

If the series k=1bk=k=11kis divergent by the power series, So k=1akalso divergence

Hence the given statement is wrong.

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