Question

chung minh rang 1/3^2+1/4^2+1/5^2+...+1/100^2<1/2

Answer 1

có: 1/3^2<1/2.3; 1/4^2<1/3.4:...: 1/100^2<1/99.100

Mà: 1/1.2+1/2.3+...+1/99.100=1-1/2+1/2-1/3+...+1/99-1/100

=1-1/100

=99/100

=> 1/3^2+1/4^2+...+1/100^2<99/100<1

=> đpcm

UNDERSTAND ???

Answer 2

đặt A= biểu thức trên

tao có 

A<1/2.3+1/3.4+...+1/99.100

A<1/2-1/3+1/3-1/4+...+1/99-1/100

A<1/2-1/100<1/2

SUY RA A<1/2(DPCM)