Question

Tìm các giới hạn sau:

\(a,lim\dfrac{3+4^n}{1+3.4^{n+1}}\)

\(b,lim\dfrac{\left(-2\right)^n+3^n}{\left(-2\right)^{n+1}+3^{n+1}}\)

Answer 1

\(\lim\dfrac{3+4^n}{1+3.4^{n+1}}=\lim\dfrac{3+4^n}{1+12.4^n}=\lim\dfrac{3\left(\dfrac{1}{4}\right)^n+1}{\left(\dfrac{1}{4}\right)^n+12}=\dfrac{0+1}{0+12}=\dfrac{1}{12}\)

\(\lim\dfrac{\left(-2\right)^n+3^n}{\left(-2\right)^{n+1}+3^{n+1}}=\lim\dfrac{\left(-2\right)^n+3^n}{-2\left(-2\right)^n+3.3^n}=\lim\dfrac{\left(-\dfrac{2}{3}\right)^n+1}{-2\left(-\dfrac{2}{3}\right)^n+3}=\dfrac{0+1}{0+3}=\dfrac{1}{3}\)