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1. Rút gọn:
$\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{(n-1)n(n+1)}$
Từ đó C/m:
$\frac{1}{3^{3}}+\frac{1}{4^{3}}+\frac{1}{5^{3}}+...+\frac{1}{(n+1)^{3}}<\frac{1}{12}$
2. CM:
a. $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2^{n}-1}> \frac{n}{2}$
b. $\frac{\sqrt{1}}{2}+\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}+...+\frac{\sqrt{n}}{n}>\sqrt{n}$
