Thread: Can you evaluate this limit? View Single Post
 $$\lim_{\Delta x\to0}\sum_{k=1}^{[\frac{x}{\Delta x}]}\frac{\Delta x}{1+(k-1)\Delta x}\\ =\lim_{n\to\infty}\sum_{k=1}^n\frac{x/n}{1+(k-1)x/n}\\ =\lim_{n\to\infty}\frac1n\sum_{k=1}^n\frac{x}{1+x(k-1)/n}\\ =\int_0^1\frac{x}{1+xu}\ du =\log(1+x)$$