Triple the fun!

Calculus Level 4

If the value of

\(\displaystyle \sum_{i = 0}^{\infty } \sum_{j = 0}^{\infty } \sum_{k= 0}^{\infty } \frac{1}{3^{i} 3^{j} 3^{k}}\)
\((i \neq j \neq k)\)

Can be represented as \(\dfrac {m}{n}\)

Then find

\(\displaystyle m \times n\)

Note: You are asked to find the summation over all ordered triplets of distinct non-negative integers.

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