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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