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Some Pig
#2
Apr15-11, 09:14 AM
P: 38
[tex]\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)[/tex]