`A=2/(3)*(4)/(5)*(6)/(7)*...*98/99 > 1/10`
Ta có:
`2/3>1/2;4/5>3/4;6/7>7/8;...;98/99>97/98`
`⇒2/(3)*(4)/(5)*(6)/(7)*...*98/99>1/2*3/4*7/8*...*99/100`
Đặt `B=1/2*3/4*7/8*...*97/98`
`⇔A>B`
`→A^2>A.B`
`→A^2>(2/(3)*(4)/(5)*(6)/(7)*...*98/99)*(1/2*3/4*7/8*...*99/100)`
`→A^2>2/3*3/4*4/5*5/6 .....98/99*99/100`
`→A^2>1/100`
`→A^2>A.B=1/99<1/100`
`→A>1/10`
