Find the sum of the following. (1 - 1/n) + (1 - 2/n) + (1 - 3/n)+..... up to n terms.

Question

Find the sum of the following.

\((1-\frac{1}{n})+(1-\frac{2}{n})+(1-\frac{3}{n})\)+..... up to n terms.

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

Answer 1

On simplifying the given series, we get:

\((1-\frac{1}{n})+(1-\frac{2}{n})+(1-\frac{3}{n})\)+.....n terms

  Here, \((\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+....+\frac{n}{n})\) is an AP whose first term is \(\frac{1}{n}\)

and the common difference is \((\frac{2}{n}-\frac{1}{n})=\frac{1}{n}.\)

The sum of terms of an AP is given by