Ta có:
Đặt `A=1/2+1/2^2+...+1/2^2014`
`2A=1+1/2+...+1/2^2013`
`2A-A=(1+1/2+...+1/2^2013)-(1/2+1/2^2+...+1/2^2014)`
`A=1-1/2^2014<1`
Vậy `A<1`
Ta có:
Đặt `B=1/2^2+1/3^2+...+1/100^2`
`C=1+ 1/2^2+1/3^2+...+1/100^2`
Theo bài ra ta có:
`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`
`=>B<1/1.2+1/2.3+...+1/99.100`
`=1-1/2+1/2-1/3+...+1/99-1/100`
`=1-1/100`
`=>``C=1+1-1/100=2-1/100<2`
Vậy `C<2`
