Sum of Infinite series $\frac{1.3}{2}+\frac{3.5}{2^2}+\frac{5.7}{2^3}+\frac{7.9}{2^4}+......$ Prove that the sum of the infinite series $\frac{1.3}{2}+\frac{3.5}{2^2}+\frac{5.7}{2^3}+\frac{7.9}{2^4}+......$ is 23.
My approach 
I got the following term
$S_n=\sum_1^\infty\frac{4n^2}{2^n}-\sum_1^\infty\frac{1}{2^n}$.
For $\sum_1^\infty\frac{1}{2^n}$ the answer is 1 as it forms a geometric series but I am bot able to find the solution to $\sum_1^\infty\frac{4n^2}{2^n}$.

Hint. One may used this
$$\sum_{n\ge1}n^{2}x^n=\frac{x}{(1-x)^{2}}+\frac{2x^{2}}{(1-x)^{3}},\qquad |x|<1,$$ proved for example here.
Hope you can take from here.
