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The integral Test :
If is positive, continuous and decreasing for and then and either both converge or both diverge.
The series is .
(a)
For .
Substitute in .
.
Therefore, the sum of the series is is diverges for .
The series is .
(b)
For .
Substitute in .
.
Therefore, the sum of the series is is diverges for .
The series is .
(c)
For .
Find the value for is converge where .
Since , consider .
.
.
.
The series is is converges if .
Therefore, the sum of the series is is converges if .
(a) The sum of the series is is diverges for .
(b) The sum of the series is is diverges for .
(c) The sum of the series is is converges if .
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