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find the sum of the series: sum from k=1 to infinity [(3/k(k+1)(k+2))+(-2/3)^k]

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i know that for 3/k(k+1)(k+2) I would use partial fraction representation

and the (-2/3)^k part is just a geometric series

S = (-2/3)/(1+2/3) = -2/5

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