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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
If $[\mathrm{x}]$ be the greatest integer less than or equal to $\mathrm{x}$, then $\sum_{\mathrm{n}=8}^{100}\left[\frac{(-1)^{n} \mathrm{n}}{2}\right]$ is equal to:
  • A
    $-2$
  • ✓
    $4$
  • C
    $2$
  • D
    $0$
✓

Answer

Correct option: B.
$4$
b
$\sum_{n=8}^{100}\left[\frac{(-1)^{n} \cdot n}{2}\right]=\left[\frac{8}{2}\right]+\left[\frac{-9}{2}\right]+\left[\frac{10}{2}\right]+\left[\frac{-11}{2}\right]+\ldots+\ldots\left[\frac{-99}{2}\right]+\left[\frac{100}{2}\right]$

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

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