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1+112(1+2)2+2+122(2+2)2+3+132(3+2)2+…=AB\frac {1+1}{1^2{(1+2)}^2} +\frac {2+1}{2^2{(2+2)}^2} +\frac {3+1}{3^2{(3+2)}^2} + \ldots = \frac{A}{B}12(1+2)21+1+22(2+2)22+1+32(3+2)23+1+…=BA
Find A+B A+B A+B where AAA and BBB are coprime positive integers.
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