Cho dãy số \(a_n=\dfrac{4.3^n+7^{n+1}}{2.5^n+7^n}\). Tính \(\lim\limits a_n\).
\(\dfrac{11}{3}\).\(7\).\(\dfrac{5}{3}\).\(2\).Hướng dẫn giải:\(a_n=\dfrac{4.3^n+7^{n+1}}{2.5^n+7^n}\)\(=\dfrac{4.3^n+7^{n+1}}{7^n}:\dfrac{2.5^n+7^n}{7^n}\)\(=\left(4.\left(\dfrac{3}{7}\right)^n+7\right):\left(2.\left(\dfrac{5}{7}\right)^n+1\right)\)
Suy ra \(\lim\limits a_n=\left(\left(4.0+7\right)\right):\left(2.0+1\right)=7.\)
