find the sum of 1 - 1n 1 - 2n 1 -

Question

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