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| PAGE: 623 | SET: Exercises | PROBLEM: 25 |
The integral Test :
If 
is positive, continuous and decreasing for 
and 
then 
and 
either both converge or both diverge.
The integral series is 
.
The summation notation of series is 
.
Let the function be 
.
Find the derivative of the function.
is positive, continuous and decreasing for 
.
satisfies the conditions of Integral Test.
Integral Test is applicable for the series.
Integral Test:
Consider 
.
.
Consider integral 
.
Substitute 
.
Apply derivative on each side with respect to 
.
.
Substitute 
and 
in .
Substitute .
.
.
Therefore, the series is diverges.
The series is diverges.
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