JEE Advanced Sequence and Series 2

Calculus Level 5

Calculate S=n=11015n(5n3n)(5n+13n+1)S=\displaystyle\sum_{n=1}^{10} \dfrac{15^n}{(5^n-3^n)(5^{n+1}-3^{n+1})}. Enter answer as 10000S\lfloor 10000S\rfloor

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