Xét A=(1/2^2-1)(1/3^3-1)(1/4^4-1)...(1/100^100-1)
=-(1-1/2^2)(1-1/3^3)(1-1/4^4)...(1-1/100^100)
>-(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/100^2)
=-(3/2²·8/3²·15/4²·...·9999/100²)
=-[(1·3)/2²·(2·4)/3²·(3·5)/4²·...·(99·101)/100²]
=-(1/2·101/100)=-101/200<-100/200=-1/2