Not easy as sum of squares -2
Algebra
Level
5
\[ \sum_{ k=1 }^\infty{ \frac { 1 }{ { k }^{ 2 } } =\frac { { \pi }^{ 2 } }{ 6 } },\qquad { S }_{ i }=\sum_{ k=1 }^\infty\frac { i }{ { \big(36{ k }^{ 2 }-1\big) }^{ i } } \]
Given the above, \(S_{1}+S_{2}\) can be represented as \(\dfrac { { \pi }^{ 2 } }{ a } -\dfrac { b }{ c } \).
Find the value of \(a+b+c\) with \(c\) a prime number.
by
Gautam Sharma