Question

CMR 1/2<1/2^2+1/3^2+...+1/200^2<3/4

Answer 1

gọi tổng đó là A

A<1/2^2 + 1/2.3+1/3.4+1/4.5...+1/199.200

A<1/2^2 + 1/2-1/3+1/3-1/4+1/4-1/5+...+1/199-1/200

A<1/2^2+1/2-1/200

A<3/4-1/200<3/4 (đpcm

để so sánh A> hơn 1/2 thì mình so sánh theo cách:

A=1/2^2+1/3^2+....+1/200^2>1/2^2+1/2^2=1/2

vậy cần so sánh 1/3^2+....+1/200^2 với 1/2^2

1/3^2+1/4^2+....+1/200^2 > 1/3.4+1/4.5+1/5.6+...+1/200.201=1/3-1/4+1/4-1/5+1/5-1/6+...+1/200-1/201=1/3-1/201=66/201>66/266=1/4

vậy là chứng minh xong