Question

If $\left[x\right]$ be the greatest integer less than or equal to $x,$ then $\sum _{n=8}^{100}\left[\frac{{(-1)}^{n}n}{2}\right]$ is equal to

• A. $2$
• B. $-2$
• C. $0$
• D. $4$

Answer 1

The correct option is D $4$

$\sum _{n=8}^{100}\left[\frac{{(-1)}^{n}n}{2}\right]$
$=4-5+5-6+6-7+7+\dots -50+50$
$=4$