Summation and Summation

Calculus Level 3

Let

\(f(s) = \displaystyle \sum_{n=0}^\infty \frac {1}{s^n}\).

If the value of

\(\displaystyle \sum_{s=2}^{10} f(s)\)

can be represented as \(\frac {A}{B}\) where \(A\) and \(B\) are positive, coprime integers, find the value of \(A + B\).

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