Sequences and series (3)

Calculus Level 5

i=0j=0k=013i 3j 3k,ijk\large \sum_{i=0}^{\infty} \sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \dfrac{1}{3^i \ 3^j \ 3^k}, \quad i≠j≠k

Find the value of the above triple summation. If your answer comes in form of ab\dfrac{a}{b} where aa and bb are positive coprime integers, then enter a+ba+b as your answer.

Note: ii, jj, and kk are distinct.


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