Question

Find the sum of the series
1/(1)(2) + 1/(2)(3) + ................1/(n-1)(n)

Answer 1

=> Sn = [1/1 - 1/2]+[1/2 - 1/3]+[1/3 - 1/4]+..
=> Sn = 1 - 1/(n+1) => Sn = n / (n + 1)
Here n = 99=> Sn = 99 / 100.