# Sequences and series (3)

Calculus Level 5

$\large \sum_{i=0}^{\infty} \sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \dfrac{1}{3^i \ 3^j \ 3^k}, \quad i≠j≠k$

Find the value of the above triple summation. If your answer comes in form of $$\dfrac{a}{b}$$ where $$a$$ and $$b$$ are positive coprime integers, then enter $$a+b$$ as your answer.

Note: $$i$$, $$j$$, and $$k$$ are distinct.

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