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 $A+B$ .