For what values of p is each series convergent?
The values of for which the given series is convergent.
Alternating Series Test:
If the alternating series
i) for all
then the series is convergent otherwise the series is divergent.
can be positive, negative, and zero. Let’s check the divergence of series for these possibilities.
The given series will be:
This verifies the first condition, which is, the given series is decreasing for
For the second condition, look for the term as .
Thus, both the conditions of the alternating series are satisfied
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