JEE Main 2021 (Online) 25th July Evening ShiftQuestion 1
If $[x]$ 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 :
Functions
Solution
Even $n$: term $\frac n2$, sum over $n=8,\dots,100$ is $4+\dots+50=1269$. Odd $n$: $\left[-\frac n2\right]=-\frac{n+1}2$, sum over $n=9,\dots,99$ is $-(5+\dots+50)=-1265$. Total $4$.