Question

tính giới hạn \(\lim\limits_{n\rightarrow\infty}\dfrac{3^n-4^{n+1}}{3^{n+2}+4^n}\)

Answer 1

\(\lim\limits_{n\rightarrow\infty}\dfrac{3^n-4^{n+1}}{3^{n+2}+4^n}\)

\(=\lim\limits_{n\rightarrow\infty}\dfrac{\dfrac{3^n}{4^{n+2}}-\dfrac{4^{n+1}}{4^{n+2}}}{\dfrac{3^{n+2}}{4^{n+2}}+\dfrac{4^n}{4^{n+2}}}\)

\(=\lim\limits_{n\rightarrow\infty}\dfrac{\dfrac{3^n}{4^n}.\dfrac{1}{4^2}-\dfrac{4^{n+1}}{4^{n+1}}.\dfrac{1}{4}}{\dfrac{3^{n+2}}{4^{n+2}}+\dfrac{4^n}{4^n}.\dfrac{1}{4^2}}=\dfrac{-\dfrac{1}{4}}{\dfrac{1}{4^2}}=-4\)