The value of displaystyle lim n arrow ∞ (1+2-3+4+5-6+ ldots .+(3 n-2)+(3 n-1)-3 n/√2 n4+4 n+3- √n4+5 n+4) is :

Question

The value of displaystyle lim n arrow ∞ (1+2-3+4+5-6+ ldots .+(3 n-2)+(3 n-1)-3 n/√2 n4+4 n+3- √n4+5 n+4) is : (A) 3(√2+1) (B) (3/2)(√2+1) (C) (√2+1/2) (D) (3/2 √2)

Tardigrade Admin · Accepted Answer

undersetn arrow ∞Lim (0+3+6+9+ ldots . n text terms /√2 n4+4 n+3-√n4+5 n+4) undersetn arrow ∞Lim (3 n(n-1)/2(√2 n4+4 n+3-√n4+5 n+4)) =(3/2(√2-1))=(3/2)(√2+1)

Q. The value of $n \to \infty lim \frac{1 + 2 - 3 + 4 + 5 - 6 + \dots . + ( 3 n - 2 ) + ( 3 n - 1 ) - 3 n}{2 n ^{4} + 4 n + 3 - n ^{4} + 5 n + 4}$ is :

$3 (2 + 1)$

$\frac{3}{2} (2 + 1)$

$\frac{2 + 1}{2}$

$\frac{3}{2 2}$

$n \to \infty L im \frac{0 + 3 + 6 + 9 + \dots . n terms}{2 n ^{4} + 4 n + 3 - n ^{4} + 5 n + 4}$
$n \to \infty L im \frac{3 n ( n - 1 )}{2 ( 2 n ^{4} + 4 n + 3 - n ^{4} + 5 n + 4 )}$
$= \frac{3}{2 ( 2 - 1 )} = \frac{3}{2} (2 + 1)$

Q. The value of n→∞lim​2n4+4n+3−​n4+5n+4​1+2−3+4+5−6+….+(3n−2)+(3n−1)−3n​ is :

3(2​+1)

23​(2​+1)

22​+1​

22​3​