Question

Find the sum of the following.

(1-1/n) + (1-2/n) + (1-3/n) + ....... up to n terms.

Answer 1

On simplifying the given series, we get:

Answer 2

\(S = (1 - \frac 1n) + (1 - \frac 2n) + (1 - \frac 3n) + .....\) upto 'n' terms

\(= (1 + 1 + ....n \text{ times}) - \frac 1n (1 + 2 + 3+.... n\text{ term})\)

\(= n - \frac 1n \times \frac{n(n + 1)}2\)

\(= n - \frac{n + 1}2\)

\(= \frac{2n - n -1}{2}\)

\(= \frac{n - 1}2\)