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113−213+23+313+23+33−413+23+33+43+⋯\frac{1}{1^3}-\frac{2}{1^3+2^3}+\frac{3}{1^3+2^3+3^3}-\frac{4}{1^3+2^3+3^3+4^3}+\cdots131−13+232+13+23+333−13+23+33+434+⋯ If the given sum equal to πAB+ClnA−C\dfrac{{\pi}^A}{B}+C\ln{A}-CBπA+ClnA−C for positive integers AAA, BBB, and CCC, find A+B+CA+B+CA+B+C.
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