Sau it nhat 28 phut

1/2^2=1/2.2<1/1.2

1/3^2=1/3.3<1/2.3

....

1/100^2=1/100.100<1/99.100

do đó 1/2^2+1/3^2+....+1/100^2<1/1.2+1/2.3+...+1/99.100

Áp dụng công thức :1/n - 1/n+1=(n+1-n)/n.(n+1)=1/n(n+1)

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

=>1/2^2+1/3^2+....+1/100^2<1(đpcm)