Find $an$ expression for the general term $of$ the following series and give the range $of$ values for the index.

$\frac{x+5}{x+2}=\frac{5}{2}-\frac{3}{4}x+\frac{3}{8}{x}^2-\frac{3}{16}{x}^3+\frac{3}{32}{x}^4-$cdots

$\frac{(-1{)}^{n}3}{2^{n+1}}{x}^n$;$n1$

$\frac{(-1{)}^{n}3}{2^{n+1}}{x}^n$;$n1$ and $\frac{5}{2}$ for $n=0$

$\frac{(-1{)}^{n}3}{2^n}{x}^n$;$n1$ and $\frac{5}{2}$ for $n=0$

$\frac{3}{2^{n+1}}{x}^n$;$n1$ and $\frac{5}{2}$ for $n=0$