# A triple summation with a restriction!

Algebra Level 5

$\large \displaystyle \sum_{i\ne j, j\ne k, k\ne i } \frac{1}{2^i 2^j 2^k} = \frac{a}{b},$
where $$i,j,k$$ are distinct whole numbers. If $$a,b$$ are coprime positive integers, determine the value of $$a+b$$.

Clarifications on the summation
The summation runs over all triples $$(i,j,k)$$ of pairwise non-negative integers. As an example, $$(1,3,2)$$ and $$(1,0,8)$$ are allowed but $$(3,3,2)$$, $$(0,0,0)$$, $$(0,0,3)$$ and $$(7,7,7)$$ aren't.

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