One of those Sums

Calculus Level 3

Select the function that expresses the value of the indicated sum \( S(\alpha ) \) for any \( \alpha \), where \( -1 \lt \alpha \lt 1 \).

\[ S(\alpha) = \sum_{k=0}^{\infty} \frac{\alpha^k}{(k+1)(k+2)} \]

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