$\\$
`5/(1.2.3)+5/(2.3.4)+...+5/(98 . 99 .100)`
`= 5 . (1/(1.2.3) +1/(2.3.4)+...+1/(98.99.100) )`
`=5 . 1/2 . (1/(1.2) - 1/(2.3)+1/(2.3) - 1/(3.4)+...+1/(98 . 99) - 1/(99 . 100) )`
`= 5/2 . (1/(1.2) - 1/(99.100) )`
`= 5/2 . (1 - 1/2 - 1/99+ 1/100)`
`= 5/2 . 4949/9900`
`= 4949/3960`