Question

Determine el valor de convergencia de la sucesión (an) tal que​

Answer 1

$L=\lim\limits_{n\to+\infty}\dfrac{\dfrac{\sqrt{3n^4+5n^2+1}+2n}{n^2}}{\dfrac{4n^2+(-1)^n}{n^2}}=\lim\limits_{x\to+\infty}\dfrac{\sqrt{3+\dfrac{5}{n^2}+\dfrac{1}{n^4}}+\dfrac{2}{n}}{4+\dfrac{(-1)^n}{n^2}}=\dfrac{\sqrt{3+0+0}+0}{4+0}\\ \\ \\L=\dfrac{\sqrt3}{4}$