`(1.2 -1)/(2!) +(2.3 -1)/(3!)+(3.4)/(4!)+...+ (99.100-1)/(100!)`
Đặt `A=(1.2 -1)/(2!) +(2.3 -1)/(3!)+(3.4)/(4!)+...+ (99.100-1)/(100!)`
`=>A=(1.2)/(2!)- 1/(2!)+ (2.3)/(3!)-1/(3!)+...+(99.100)/(100!)-1/(100!)`
`=>A=[((1.2)/(2!)+(2.3)/(3!)+....+(99.100)/(100!))-(1/(2!)+1/(3!)+...+1/(100!)]`
`=>A=[(1+1+1/(2!)+....+1/(98!))-(1/(2!)+1/(3!)+...+1/(100!)]`
`=>A=1-1/(99!)-1/(100!)`
Mà `1-1/(99!)-1/(100!)<1=>1-1/(99!)-1/(100!)<2` `->đpcm`