Question

[Phan Thuý An]

chứng minh\(\frac{1}{2^2}+\frac{1}{3^2}+.............+\frac{1}{100^2}< 1\)

Answer 1

[TRẦN MINH NGỌC]

1 /2² +1/ 3² +.......+ 1/ 100² < 1/ 1. 2 + 1 / 2 .3 + 1 / 3. 4 + ......  + 1 / 99 .100

= 1- 1 / 2 + 1 / 2 - 1/ 3 + 1 / 3 - 1 / 4 +......+ 1 / 99 - 1 / 100

= 1 - 1 / 100< 1

=> 1 /2² +1/ 3² +.......+ 1/ 100² < 1 ( đpcm)