(Solved):   Find the Maclaurin series for \( f(x) \) using the definition of a Maclaurin series \[ \be ...

 

Find the Maclaurin series for \( f(x) \) using the definition of a Maclaurin series \[ \begin{array}{c} f(x)=\ln (1+5 x) \\ \left.f(x)=\sum_{n=1}^{\infty}(-1)^{n+1} \frac{(x-5)^{n}}{n}\right)_{x} \end{array} \] Find the associated radius of convergence \( R \).