An algebra problem by Lakshya Sinha

Algebra Level 5

$\large{\frac { 1 }{ 1\times 2\times 9 } +\frac { 1 }{ 4\times 3\times 16 } +\frac { 1 }{ 9\times 4\times 25 } +\cdots}$

Let $$S$$ represent the infinite summation above. Find $$S^{-497} \mod{7}$$

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