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Find limit of S_n - [Iran Second Round 1984]

Source:

December 30, 2010
limitalgebra unsolvedalgebra

Problem Statement

Suppose that Sn=59×1420×2735×⋯×2n2−n−12n2+n−1S_n=\frac 59 \times \frac{14}{20} \times \frac{27}{35} \times \cdots \times \frac{2n^2-n-1}{2n^2+n-1} Find lim⁡n→∞Sn.\lim_{n \to \infty} S_n.
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