Question

tính giới hạn \(\lim\limits_{n\rightarrow\infty}\dfrac{7^n+2^n}{3.7^n+4^n}\)

Answer 1

\(\lim\limits_{n\rightarrow\infty}\dfrac{7^n+2^n}{3\cdot7^n+4^n}\)

\(=\lim\limits_{n\rightarrow\infty}\dfrac{\dfrac{7^n}{7^n}+\dfrac{2^n}{7^n}}{3\cdot\dfrac{7^n}{7^n}+\dfrac{4^n}{7^n}}\)

\(=\lim\limits_{n\rightarrow\infty}\dfrac{1+\left(\dfrac{2}{7}\right)^n}{3+\left(\dfrac{4}{7}\right)^n}\)

\(=\dfrac{1+0}{3+0}=\dfrac{1}{3}\)

Answer 2

\(lim\dfrac{7^n+2^n}{3.7^n+4^n}=lim\dfrac{\dfrac{7^n}{7^n}+\dfrac{2^n}{7^n}}{\dfrac{3.7^n}{7^n}+\dfrac{4^n}{7^n}}=lim\dfrac{1+\left(\dfrac{2}{7}\right)^n}{3+\left(\dfrac{4}{7}\right)^n}=\dfrac{1}{3}\)