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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
The value of $\mathop {\lim }\limits_{n\, \to \,\infty } \frac{{1 - {n^2}}}{{\sum n}}$ will be
  • ✓
    $-2$
  • B
    $-1$
  • C
    $2$
  • D
    $1$
✓

Answer

Correct option: A.
$-2$
a
(a) $\mathop {\lim }\limits_{n \to \infty } \,\frac{{1 - {n^2}}}{{\Sigma n}}$ $ = \mathop {\lim }\limits_{n \to \infty } \frac{{(1 - n)(1 + n)}}{{\frac{1}{2}n(n + 1)}}$

$ = \mathop {\lim }\limits_{n \to \infty } \,\frac{{2\,(1 - n)}}{n}$

$ = \mathop {\lim }\limits_{n \to \infty } 2\,\left( {\frac{1}{n} - 1} \right)$$ = 2(0 - 1) = - 2$.

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