AP/GP

Algebra Level 4

$\large \dfrac{1 \times 2}{10} + \dfrac{2 \times 3}{10^2} + \dfrac{3 \times 4}{10^3} + \dfrac{4 \times 5}{10^4} + \ldots$

If the value of the series above can be expressed as $$\dfrac{A}{B}$$, where $$A$$ and $$B$$ are coprime positive integers, find the value of $$A+B$$.

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