Determining Convergence or Divergence
In Exercises 9-30, determine the convergence or divergence of the series.
Given: The series .
Formula used: The Alternating Series test
Let . The alternating series
and converges when the following two conditions hold good.
1. , and
Absolute and conditional convergence test explain that
3. The series is absolutely convergent when the series is convergent.
4. The series is conditionally convergent when the series is convergent but the series is divergents.
Calculation: Here, let us consider the series . Since the series has both positive and negative elements, it can be concluded that the series is an alternating series.
Here . Since for all positive n and goes to zero as goes to , so the first condition of alternating series test is held true.
The given series is monotonically decreasing for all n greater than 1, hence it also holds the second criteria of the alternating series test
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