The series is .
Alternating Series Test:
If the alternating series satisfies
(i) .
(ii) .
then the series is convergent.
Verify condition (i) :
Consider the related function .
Differentiate the function with respect to x .
.
Since we are considering only positive , consider .
.
For , .
Verify condition (ii):
Apply L-hospital rule to find the limit.
LHospitals Rule :
If the value of limit is indeterminate form of type or , then
.
Series satisfies conditions of alternating series test.
Thus, the series is convergent.
The series is convergent.
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