Question

The sum of the products of the $2n$ numbers $\pm 1,\pm 2,\pm 3,.....,\pm$ $n$ taking two at time is

• A. $\frac{n(n+1)}{2}$
• B. $\frac{n(n+1)(2n+1)}{6}$
• C. $\frac{-n(n+1)(2n+1)}{6}$
• D. $\frac{-n(n+1)}{2}$

Answer 1

The correct option is C $\frac{-n(n+1)(2n+1)}{6}$

$1\times (-1)+2\times (-2)+3\times (-3)+\dots \dots ..+n\times (-n)$

Then answer follows

$1\times (-1)+2\times (-2)+3\times (-3)+\dots .+n\times (-n)=-1^2-2^2-3^2....-n^2=-(1^2+2^2+3^2...+n^2)=-\frac{n(n+1)(2n+1)}{6}$