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Algebra Level 4

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

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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