Use the Divergence Test to determine whether the following series diverge or state that the test is inconclusive.
Given :
Series is :
To determine:
If the series diverges or not using Divergence test.
Solution:
Divergence Test:
According to this test, if we take the limit of the general term of the series and if that limit is not equal to 0, then the series diverges. And , also if that limit is equal to 0, then it does not mean that the series converges, it simply states that the test is failed or inconclusive.
Let's use:
Divergence test to determine whether the given series diverges=?
Given series is :
Hence,
Let's take the limit of the given series :
Hence,
Therefore,
Divergence test fails here, or, the given test is inconclusive.
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