Sum of arithmetico-geometric series

Find the sum of $n$ terms of the series the $r^{th}$ term of which is $(2 r + 1) 2^{r}$ .

~10 minAnswer checked instantlyseriesgeometric progressionsummation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 19

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).