Question

1 . 

a) 1/2 + 1/6 + 1/12 +....+1/x.(x+1) = 99/100

Answer 1

`1/2+1/6+1/12+....+1/(x(x+1))=99/100`

`-> 1/(1.2)+1/(2.3)+1/(3.4)+....+1/(x(x+1))=99/100`

`-> 1 - 1/2 + 1/2 -1/3 +1/3-1/4+....+1/x -1/(x+1)=99/100`

`-> 1-1/(x+1)=99/100`

`-> x/(x+1)=99/(99+1)`

`-> x=99`