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)}}$
(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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