# 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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