Chứng tỏ rằng: 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/10^2 < 1

* Hướng dẫn giải

$\frac{1}{2^2} <\frac{1}{1.2};\frac{1}{3^2}<\frac{1}{2.3};\frac{1}{4^2}<\frac{1}{3.4};\mathrm{...};\frac{1}{{10}^2}<\frac{1}{9.10}$

$\Rightarrow \frac{1}{2^2} +\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{{10}^2}<\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\mathrm{...}+\frac{1}{9.10}<1.$