Find the value of \( S_{n}=\sum_{n=1}^{n} \frac{3^{n} \cdot 5^{n}}{...

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Find the value of \( S_{n}=\sum_{n=1}^{n} \frac{3^{n} \cdot 5^{n}}{\left(5^{n}-3^{n}\right)\left(5^{n+1}-3^{n+1}\right)} \) and hence \( S_{\infty} \).
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