Question

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

Answer 1

Answer:

(n - 1)/2

Step-by-step explanation:

F = (1 - 1/n) + (1 - 2/n) + (1 - 3/n) + ...(1 - n/n)

  = (1 + 1 ... + 1) - (1/n + 2/n + 3/n + ...n/n)

     (there are n terms of 1)

  = n - (1 + 2 + 3 + ... + n)/n

  = n - [n x (n + 1)/2]/n

  = n - [n x (n + 1)]/[2 x n]

  = n - (n+1)/2

  = (2n - n - 1)/2

  = (n - 1)/2

Hope this helps!