Question

Tính giới hạn \(\lim\limits_{n\rightarrow\infty}\left(\dfrac{3^n-4.2^{n+1}-3}{3.2^n+4^n}\right)\)

Answer 1

\(\lim\limits_{n\rightarrow\infty}\left(\dfrac{3^n-4\cdot2^{n+1}-3}{3\cdot2^n+4^n}\right)\)

\(=\lim\limits_{n\rightarrow\infty}\left(\dfrac{3^n-3-8\cdot2^n}{3\cdot2^n+4^n}\right)\)

\(=\lim\limits_{n\rightarrow\infty}\left(\dfrac{\dfrac{3^n}{4^n}-\dfrac{3}{4^n}-8\cdot\left(\dfrac{2}{4}\right)^n}{3\cdot\left(\dfrac{2}{4}\right)^n+\left(\dfrac{4}{4}\right)^n}\right)\)

\(=\dfrac{0-0-8\cdot0}{3\cdot0+1}=0\)