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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