# Triple sum

Calculus Level 5

$\large S= \sum^{\infty}_{i=0}\sum^{\infty}_{j=0}\sum^{\infty}_{k=0} \dfrac{1}{5^{i+j+k}}, \quad i≠j≠k, i≠k$ If the value of $$S$$ is in the form $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, then find $$a+b$$.

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