Only evens allowed

Calculus Level 3

Let \( S_n = \frac{1}{1} + \frac {1}{2} + \frac {1}{2 \times 4} + \ldots + \frac { 1 } { 2 \times 4 \times \cdots \times 2n } \). Evaluate

\[ \lim_{n\rightarrow \infty} S_n .\]

Details and assumptions

Note: The initial term \( \frac {1}{1} \) occurs because the empty product (product of no terms) is defined to be 1.

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