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Algebra Level 4

S=1×2210+2×32102+3×42103+4×52104+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 SS is in the form AB\dfrac{A}{B}, where AA and BB are coprime positive integers, find the value of A+BA+B.

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