` P = 4/(1.2) + 4/(2.3) + ............... + 4/(99.100)`
`1/4P = 1/(1.2) + 1/(2.3) + ........... + 1/(99.100)`
`1/4P = 1 - 1/2 + 1/2 - 1/3 + .................. + 1/99 - 1/100`
`1/4P = 99/100`
`⇒ P = 99/100 : 1/4 = 99/25`
`S = 1/(x.(x+1)) + 1/((x + 1).(x + 2)) + ............... + 1/((x+99).(x+100)`
`S = 1/x - 1/(x +1) + 1/(x + 1) - 1/(x + 2) + ............. + 1/(x + 99) - 1/(x + 100)`
`S = 1/x - 1/(x + 100)`