Question

CMR: \(\dfrac{1}{4}\)+\(\dfrac{1}{16}\) + \(\dfrac{1}{36}\) +....+ \(\dfrac{1}{10000}\) < \(_{\dfrac{1}{2}}\)

Answer 1

Đặt `A= 1/4 + 1/16 + 1/36 +...+ 1/10000`

`A= 1/4 ( 1 + 1/4 + 1/9 + ...+ 1/2500)`

`A= 1/4 ( 1 + 1/2.2 + 1/3.3 +...+ 1/50.50)`

`A < 1/4 ( 1 + 1/1.2 + 1/2.3 +...+ 1/49.50)`

`A< 1/4( 1+ 1/1 - 1/2 + 1/2 -1/3 +... + 1/49 - 1/50)`

`A< 1/4 ( 1 + 1 - 1/50)`

`A< 1/4 ( 2 - 1/50)`

`A< 1/2 - 1/200 < 1/2`