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A limit of a power series [entire topic moved to new forum]

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Evaluate the following limit:

$$\lim_{x \rightarrow 1-} \sum_{n=0}^{\infty} (-1)^n \frac{2^{2 n}}{\binom{2 n}{n}} x^{2 n}$$

Answer:  \( \displaystyle \frac{1}{2} \left (1-\frac{\log{(1+\sqrt{2})}}{\sqrt{2}} \right ) \)

Tags: #Limits
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