If [x] be the greatest integer less than or equal to x,

Question:

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:

  1. 0

  2. 4

  3. -2

  4. 2


Correct Option: , 2

Solution:

$\sum_{n=8}^{100}\left[\frac{(-1)^{n} \cdot n}{2}\right]$

$=4-5+5-6+6+\ldots-50+50=4$

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