Question

$li{m}_{n\to \infty }$ $\frac{n\left(\right(2n+1{)}^2)}{(n+2)(n^2+3n-1)}$ =

• A. 0
• B. 2
• C. 4
• D. ∞

Answer 1

The correct option is C

4

$li{m}_{n\to \infty }$ $\frac{n(2n+1{)}^2}{(n+2)(n^2+3n-1)}$
= $li{m}_{n\to \infty }$$\frac{({4n}^3+{4n}^2+n)}{(n^3+{5n}^2+5n-2)}$
=$li{m}_{n\to \infty }$ $\frac{n^3\times (4+\frac{4}{n}+\frac{1}{n^2})}{n^3(1+\frac{5}{n}+\frac{5}{n^2}-\frac{2}{n^3})}$ =4