Sum the Powers

Algebra Level 2

\(\dfrac{1}{1+2+2^2}+\dfrac{1}{2+2^2+2^3}+\dfrac{1}{2^2+2^3+2^4}+\dfrac{1}{2^3+2^4+2^5}+.... = \dfrac{a}{b}\)

For coprime \(a\) and \(b\).

Find \(a+b\)

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