`A=1/2 . 3/4 . 5/6 . ... . 9999/10000`
Gọi `B=2/3 . 4/5 . 6/7 . ... . 10000/10001`
Ta có : `A=1/2 . 3/4 . 5/6 . ... . 9999/10000<B=2/3 . 4/5 . 6/7 . ... . 10000/10001`
`=>A.A^2<A.B`
`=>A^2<1/2 . 3/4 . 5/6 . ... . 9999/10000 . 10000/10001`
`=>A^2<1/10001<1/10000`
Ta có : `1/10000=1/100 . 1/100=(1/100)^2`
`=>A^2<(1/100)^2`
`=>A<1/100`
Vậy `A=1/2 . 3/4 . 5/6 . ... . 9999/10000<1/100`
