Question

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

• A. $n$
• B. $\frac{n(n+1)}{2}$
• C. $\frac{n}{2}$
• D. $2n$

Answer 1

The correct option is C $\frac{n}{2}$

$(1-(\frac{1}{n+1}\left)\right)+(1-(\frac{2}{n+1}\left)\right)+......+1-\left(\frac{n}{n+1}\right)=n-\left[\right(\frac{1+2+3+...+n}{n+1}\left)\right]=n-\left(\frac{\left(\frac{n(n+1)}{2}\right)}{n+1}\right)n-\left(\frac{n}{2}\right)=\left(\frac{n}{2}\right)$