Triple the fun!

Calculus Level 4

If the value of

i=0j=0k=013i3j3k\displaystyle \sum_{i = 0}^{\infty } \sum_{j = 0}^{\infty } \sum_{k= 0}^{\infty } \frac{1}{3^{i} 3^{j} 3^{k}}
(ijk)(i \neq j \neq k)

Can be represented as mn\dfrac {m}{n}

Then find

m×n\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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