S=1/4+1/9+1/16+...+1/10000 chứng tỏ S<1

* Hướng dẫn giải

S=$\frac{1}{4}$+$\frac{1}{9}$+$\frac{1}{16}$+...+$\frac{1}{10000}$

 = $\frac{1}{2}$x 2 + $\frac{1}{3}$x3+...+$\frac{1}{100}$x100 < $\frac{1}{1}$x2 + $\frac{1}{2}$x3 +...+ $\frac{1}{9}$x10

= 1$-\frac{1}{2}$ + $\frac{1}{2}-\frac{1}{3}$ +...+ $\frac{1}{9}-\frac{1}{10}$ = 1$-\frac{1}{10}$ < 1