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

- Hướng dẫn giải

S=1/4+1/9+1/16+...+1/10000

 = 1/2x 2 + 1/3x3+...+1/100x100 < 1/1x2 + 1/2x3 +...+ 1/9x10

= 1 - 1/2 + 1/2 - 1/3 +...+ 1/9 - 1/10 = 1- 1/10 < 1