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$S=\dfrac{1×2^2}{10}+\dfrac{2×3^2}{10^2}+\dfrac{3×4^2}{10^3}+\dfrac{4×5^2}{10^4}+\cdots$

If $S$ is in the form $\dfrac{A}{B}$, where $A$ and $B$ are coprime positive integers, find the value of $A+B$.

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