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∑r=1∞r(r+1)3r \displaystyle\sum _{ r=1 }^{ \infty }{ \frac { r\left( r+1 \right) }{ { 3 }^{ r } } } r=1∑∞3rr(r+1)
If the summation above equals to mn \frac m n nm for coprime positive integers m,nm,nm,n, what is the value of m+nm+nm+n?
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