Word Count : 366

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We are asked to determine the values of $x$ for which the series $$ \sum_{n=1}^{\infty} \frac{1 \cdot 3 \cdot 5 \cdots (2n-1)}{2 \cdot 4 \cdot 6 \cdots 2n} \cdot \frac{x^n}{n} $$ is convergent. --- Step 1: Rewrite the factorial product as a ratio of factorials. $$ \frac{1 \cdot 3 \cdot 5 \cdots (2n-1)}{2 \cdot 4 \cdot 6 \cdots 2n} = \frac{(2n)!}{2^n n! \cdot 2 \cdot 4 \cdot 6 \cdots 2n}? $$ Actually, note: ______ ____ __________ _________ _______ ____ ________ ____ __________ ________ __________ ______.
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