MCQ
$\lim_\limits{\text{n} \rightarrow \infty}\frac{\text{n}(2\text{n}+1)2}{(\text{n}+2)(\text{n}2+3\text{n}−1)}$ is equal to:
- A0
- B2
- C4
- D$ \infty$
Solution:
$=\lim_\limits{\text{n} \rightarrow \infty}\frac{\text{n}(2\text{n}+1)2}{(\text{n}+2)(\text{n}2+3\text{n}−1)}$
$ = \displaystyle \lim_{\text{n}\to\infty}{\displaystyle \frac {\left(2+\Large \frac{1}{\text{n}} \right)^2}{\left(1+\Large \frac{2}{\text{n}} \right)\left(1+\Large \frac{3}{\text{n}} - \Large \frac{1}{\text{n}^2} \right)} }=\text{n}$
$ = \displaystyle \frac{(2+0)^2}{(1+0)(1+0+0)}$
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