-) Show that, for any positive integer n, \frac{n^{2}+3 n}{2^{n}}=\alpha n(n-1)\left(\frac{1}{2}\right)^{n-2}+\beta n\left(\frac{1}{2}\right)^{n-1} \text { for some } \alpha, \beta>0 \text {. Give the values of } \alpha \text { and

} \beta \text {. } \text { (b) Find the sum the series } \sum_{n=0}^{\infty} \frac{n^{2}+3 n}{2^{n}} \text {. }