How to compute this series: $ $ \sum_{k=0}^\infty \frac{C_k}{2^{2k+1}}$ $ where $ C_k$ is the catalan number: $ C_k=\frac{1}{k+1}{2k \choose k}$ . (Further, is there any general method to treat this question with general $ C_k$ ?)

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# How to compute this series: $\sum_{k=0}^\infty \frac{C_k}{2^{2k+1}}$

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How to compute this series: $ $ \sum_{k=0}^\infty \frac{C_k}{2^{2k+1}}$ $ where $ C_k$ is the catalan number: $ C_k=\frac{1}{k+1}{2k \choose k}$ . (Further, is there any general method to treat this question with general $ C_k$ ?)

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