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12×2210+22×32102+32×42103+42×52104+⋯\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}+\cdots1012×22+10222×32+10332×42+10442×52+⋯
If the value of the series above is equal to AB \dfrac ABBA, where AAA and BBB are coprime positive integers, find A+BA+BA+B.
if you think the series does not converge, submit your answer as 2016.
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