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JEE Main 202125 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2021 · 25 July · Evening Shift · Mathematics · Functions

If [x] be the greatest integer less than or equal to x, then ∑ _ n...

If [x]\left[x\right] be the greatest integer less than or equal to x,x, then ∑n=8100\mathop{∑}_{n = 8}^{100}\left[\dfrac{{\left(- 1\right)}^{n}n}{2}\right] is equal to:

Options

  1. A00
  2. B44
  3. C−2- 2
  4. D22

Correct answer

B. 44

Step-by-step solution

Let S=∑n=8100[(−1)n⋅n2]S = \mathop{∑}_{n = 8}^{100}\left[\dfrac{{\left(- 1\right)}^{n} \cdot n}{2}\right]

Therefore, S=4−5+5−6+6+…−50+50S = 4 - 5 + 5 - 6 + 6 + \ldots - 50 + 50

⇒S=4.⇒ S = 4 .

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