Question
Find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum.$$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{2^{n} n}$$
Step 1
The general form of an alternating series is $\sum_{n=1}^{\infty}(-1)^{n+1} a_n$ where $a_n$ is a sequence of positive terms that decreases to zero. In this case, $a_n = \frac{1}{2^{n} n}$. Show more…
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Find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. $$ \sum_{n=0}^{\infty}(-1)^{n} \frac{1}{2 n+1} $$
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