If [x] be the greatest integer less than or equal to x, then [_n = 8^100 [ ( - 1)^nn 2 ] ]…

Question

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

then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$ is equal to :

Accepted Answer

$$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$

= [4] + [-4.5] + [5] + [-5.5] + [6] +..... + [-49.5] + [50]

= 4 - 5 + 5 - 6 + 6 ......-50 + 50

= 4

Solutions · 1