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 \(A+B\).