Question

1/101+1/102+.....+1/299+1/300>2/3

Answer 1

Đặt A=1/101+1/102+1/103+...+1/300
vì 1/101>1/102>1/103>...>1/300
=>(1/101+1/102+1/103+...+1/200)+(1/201+1/202+1/103+...+1/300) > (1/200+1/200+1/200+...+1/200)+(1/300+1/300+1/300+...+1/300) 
=>1/101+1/102+1/103+...+1/300 > (1/200).100 + (1/300).100
=> A > 1/2+1/3
=> A > 5/6 
Mà 5/6>2/3
=> A > 2/3
Vậy 1/101+1/102+1/103+...+1/300 >2/3