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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