Find the sum of (1 - 1/n ) + (1 - 2/n ) + (1 - 3/n ) ....... upto n terms.
Ans:
(1 - 1/n ) + (1 - 2/n ) - upto n terms
⇒[1+1+.......+n terms] - [ 1/n + 2/n +....+ n terms]
n -[S_{n} up to n terms]
Sn = n/2[2a+(n-1)d] (d = 1/n , a = 1/n )
= n/2 = [2/n +(n-1) 1/n]
= n + 1/2
(on simplifying)
n - (n + 1)/2 =
= n - 1/2 Ans