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| PAGE: 751 | SET: Exercises | PROBLEM: 38 |
The series is 
.
Limit comparison Test :
Suppose that 
and 
are series with positive terms.
If 
, where 
is a finite number and 
, then either both series converges or both series diverges.
The dominant part of the numerator is 
and the dominant part of the denominator is 
.
Compare the given series with the series 
.
Consider 
.
Find 
.
.
Therefore, 
and 
either both converges or diverges.
The series is converges if and only if is converges.
The series is in the form of 
-series.
The -series is 
, if 
, then the series is converges.
is converges, if and only if 
.
The series is converges if and only if .
The series is converges if and only if .
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