Question

Chứng tỏ rằng:1/3^2+1/4^2+1/5^2+...+1/100^2<1/2

Answer 1

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

=>1/3^2+1/4^2+1/5^2+......+1/100^2

< 1/2.3+1/3.4+1/4.5+.....+1/99.100

=1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100

=1/2-1/100

=49/100

Mà 49/100<1/2

Nên 1/3^2+1/4^2+1/5^2+......+1/100^2<1/2

Đ ú n g nha......................