Đáp án:
`+)`
Ta có :
`1/3^2 > 1/3.4`
`1/4^2 > 1/4.5`
`...`
`1/100^2 > 1/100.101`
`to 1/3^2+1/4^2+...+1/100^2>1/3.4+1/4.5+...+1/100.101`
`to A>1/3-1/4+1/4-1/5+...+1/100-1/101>1/3 \ \ \ (1)`
`+)`
Ta có :
`1/3^2 < 1/2.3`
`1/4^2 < 1/3.4`
`...`
`1/100^2 < 1/99.100`
`to 1/3^2+1/4^2+...+1/100^2<1/2.3+1/3.4+...+1/99.100`
`to A<1/2-1/3+1/3-1/4+...+1/99-1/100`
`to A<1/2-1/100<1/2 \ \ \ (2)`
Từ `(1)` và `(2)``=> 1/3<A<1/2`
