`A= \frac{1}{2xx3} + \frac{1}{3xx4} + \frac{1}{4xx5} + ... + \frac{1}{98xx99}`
`= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ..... + 1/98 - 1/99`
`= 1/2 - 1/99`
`= 97/198`
Ta có :
`1/5 =\frac{1 xx 198}{5xx198}= 198/990`
`97/198 = \frac{97 xx 5}{198 xx 5} = 485/990`
`2/5 = \frac{2 xx 198}{5xx 198} =396/990`
Mà `198/990 <396/990 < 485/990`
⇒ `1/5 < 2/5 < A`