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∑k=1∞1k2=π26,Si=∑k=1∞i(36k2−1)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 } } k=1∑∞k21=6π2,Si=k=1∑∞(36k2−1)ii
Given the above, S1+S2S_{1}+S_{2}S1+S2 can be represented as π2a−bc\dfrac { { \pi }^{ 2 } }{ a } -\dfrac { b }{ c } aπ2−cb.
Find the value of a+b+ca+b+ca+b+c with ccc a prime number.
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