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∑n=1∞2n−1n(n+1)(n+2) \large \displaystyle\sum_{n=1}^{\infty}\frac{2n-1}{n(n+1)(n+2)}n=1∑∞n(n+1)(n+2)2n−1
If the summation above equals to AB\dfrac AB BA, where AAA and BBB are coprime positive integers, find A+BA+BA+B.
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