# 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.