QJEEM21Mae528: JEE Main 2021 Mathematics - Class 11 JEEM21Mae528 Solution: If [x] be the greatest integer less than or equal to x, then is …

Question

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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

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