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If the sum of the series (1/2-1/3)+(1/2^...

If the sum of the series `(1/2-1/3)+(1/2^2-1/(2.3)+1/3^2)+(1/2^3-1/(2^2 .3)+1/(2.3^2)-1/3^3)+(1/2^4-1/(2^3 .3)+1/(2^2 . 3^2)-1/(2. 3^3) +1/3^4)+. . .` is `alpha/beta` where `alpha and beta` are co-prime, then `alpha+3beta` is equal to _____

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