# Not easy as sum of squares -2

Algebra Level 5

Given that $$\sum_{ k=1 }^\infty{ \frac { 1 }{ { k }^{ 2 } } =\frac { { \pi }^{ 2 } }{ 6 } }$$ and if ${ S }_{ i }=\sum_{ k=1 }^\infty\frac { i }{ { (36{ k }^{ 2 }-1) }^{ i } } ,$ then $$S_{1}+S_{2}$$ can be represented as $$\frac { { \pi }^{ 2 } }{ a } -\frac { b }{ c }$$.

Find the value of $$a+b+c$$, for $$c$$ being a prime number.

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