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Calculus Level 5

$\dfrac{1^2\times2^2}{10}+\dfrac{2^2\times3^2}{10^2}+\dfrac{3^2\times4^2}{10^3}+\dfrac{4^2\times5^2}{10^4}+\cdots$

If the value of the series above is equal to $\dfrac AB$ , where $A$ and $B$ are coprime positive integers, find $A+B$ .

if you think the series does not converge, submit your answer as 2016.