Question

$(1-\frac{1}{n})+(1-\frac{2}{n})+(1-\frac{3}{n})+....uptonterms=$?

• A. $\frac{1}{2}n$
• B. $\frac{1}{2}(n-1)$
• C. $\frac{1}{2}n(n-1)$
• D. None of these

Answer 1

The correct option is B $\frac{1}{2}(n-1)$

Given sum $=(1+1+1+.....tonterms)-(\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+....tonterms)$
$=n-\frac{n}{2}(\frac{1}{n}+1)$ [Ref: nth terms $=\left(n/n\right)=1$]
$=n-\frac{n+1}{2}$
$=\frac{1}{2}(n-1)$