Not easy as sum of squares -2

Algebra Level 5

k=11k2=π26,Si=k=1i(36k21)i \sum_{ k=1 }^\infty{ \frac { 1 }{ { k }^{ 2 } } =\frac { { \pi }^{ 2 } }{ 6 } },\qquad { S }_{ i }=\sum_{ k=1 }^\infty\frac { i }{ { \big(36{ k }^{ 2 }-1\big) }^{ i } }

Given the above, S1+S2S_{1}+S_{2} can be represented as π2abc\dfrac { { \pi }^{ 2 } }{ a } -\dfrac { b }{ c } .

Find the value of a+b+ca+b+c with cc a prime number.

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