$\lim_{x \rightarrow 0} {\frac{1}{x}\left( f(x)+f(\frac{x}{2})+\cdots+f(\frac{x}{n})\right)}$ [closed]
Taking limits for individual terms and adding them up we see that the limit is $f'(0)[1+\frac 1 2+\frac 1n+\cdots+\frac 1n]$.
$\lim_{x \rightarrow 0} {\frac{1}{x}\left( f(x)+f(\frac{x}{2})+\cdots+f(\frac{x}{n})\right)}$ [closed]
Taking limits for individual terms and adding them up we see that the limit is $f'(0)[1+\frac 1 2+\frac 1n+\cdots+\frac 1n]$.