Question
Find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum.$$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{2^{n}}{5^{n} n}$$
Step 1
Step 1: First, we observe the given series: $$ \sum_{n=1}^{\infty}(-1)^{n+1} \frac{2^{n}}{5^{n} n} $$ We can see that this series is an alternating series where the terms decrease in magnitude. Show more…
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