displaystyle lim x arrow ∞ (1-2+3-4+5-6+⋅s-2 n/√n2+1+√4 n2-1) is equal to:

Question

displaystyle lim x arrow ∞ (1-2+3-4+5-6+⋅s-2 n/√n2+1+√4 n2-1) is equal to: (A) (1/3) (B) -(1/3) (C) -(1/5) (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow ∞ (1-2+3-4+5-6+⋅s-2 n/√n2+1+√4 n2-1) = displaystyle lim x arrow ∞ (-1-1-1 ⋅s n text times /√n2+1+√4 n2-1) = displaystyle lim x arrow ∞ (-1/√1+(1)n2+√4-(1)n2=-(1/3)

Q. $x \to \infty lim \frac{1 - 2 + 3 - 4 + 5 - 6 + \dots - 2 n}{n ^{2} + 1 + 4 n ^{2} - 1}$ is equal to:

$\frac{1}{3}$

$- \frac{1}{3}$

$- \frac{1}{5}$

None of these

$x \to \infty lim \frac{1 - 2 + 3 - 4 + 5 - 6 + \dots - 2 n}{n ^{2} + 1 + 4 n ^{2} - 1}$
$= x \to \infty lim \frac{- 1 - 1 - 1 \dots n times}{n ^{2} + 1 + 4 n ^{2} - 1}$
$= x \to \infty lim \frac{- 1}{1 + \frac{1}{n ^{2}} + 4 - \frac{1}{n ^{2}}} = - \frac{1}{3}$

Q. x→∞lim​n2+1​+4n2−1​1−2+3−4+5−6+⋯−2n​ is equal to:

31​

−31​

−51​