(Solved): Find the nth Maclaurin polynomial for the function. f(x)=x+12x,n=4P4(x)=2x2x2+2x32x4+3x ...

Find the $n$th Maclaurin polynomial for the function. $\begin{array}{c}f(x)=\frac{2x}{x+1},n=4\\ P_4(x)=2x?2x^2+2x^3?2x^4+3x^5\end{array}$ [-/1 Points] LARCALC12 9.8.038. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. answer is a finite set of values, enter your answers as a comma-separated list of values.) ${?}_{n=1}^{?}\frac{n!(x+6{)}^n}{1?3?5?(2n?1)}$