400 Followers Problem

Algebra Level 4

\[\large \displaystyle \sum^{10}_{n=1}\dfrac{2^{n-1}}{1+2^n+2^{n+1}+2^{2n+1}} \] If the summation above is equal to \( \dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find the value of \(A+B\).

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