Question: Find the interval of convergence of

(a) \(f\left( x \right)\)

(b) \(f'\left( x \right)\)

(c) \(f''\left( x \right)\)

(d) \(\int{f\left( x \right)dx}\)

Also check for convergence at the end points of the interval

\[f\left( x \right)=\sum\limits_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n+1}}{{\left( x-2 \right)}^{n}}}{n}}\]