Question

Chứng minh rằng: 1/5+1/20+1/21+1/22+1/23+1/24+1/25+1/101+1/102+1/103+1/104 +1/105<1/2

Answer 1

1/5+(1/20+1/21+1/22+1/23+1/24+1/25)+(1/101+1/102+103+104+105)
Ta thấy 1/21;1/22;1/23;1/24;1/25 đều nhỏ hơn 1/20 nên
1/21+1/22+1/23+1/24+1/25<5×1/20<1/4
Tương tự
1/101+1/102+1/103+1/104+1/105<5×1/100<1/20
1/5+1/20+1/20=6/20=3/10

1/5+(<1/4)+(<1/20)<1/2
1/2=5/10
3/10<5/10 vậy suy ra điều cần chứng minh