Ta có:
`1/4<1/(4-1)=1/1.3`
`1/16<1/(16-1)=1/15=1/3.5`
`1/36<1/[36-1]=1/35=1/5.7`
`1/64<1/[64-1]=1/63=7.9`
`1/100<1/[100-1]=1/99=1/9.11`
`1/144<1/[144-1]=1/143=11.13`
`1/196<1/[196-1]=1/195=1/13.15`
`=>A<1/1.3+1/3.5+1/5.7+1/7.9+1/9.11+1/11.13+1/13.15`
`=>A<1/2(2/1.3+2/3.5+2/5.7+2/7.9+2/9.11+2/11.13+2/13.15)`
`=>A<1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)`
`=>A<1/2(1-1/15)`
`=>A<1/2(15/15-1/15)`
`=>A<1/2. 14/15`
`=>A<7/15<1/2`
Vậy `A<1/2`