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An amazing summation!

Calculus Level 1

$\large\dfrac1{1\cdot2}+\dfrac1{3\cdot4}+\dfrac1{5\cdot6}+\dfrac1{7\cdot8}+\ldots$

Let $S$ denote the value of series above. Find the value of $e^S$ .

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by Ikkyu San

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