Question

tìm lim\(\dfrac{2^n\left(4^{n+1}-3^{n+2}-1\right)}{5^n+8^n}\)

Answer 1

\(\lim\dfrac{2^{n}(4^{n+1}-3^{n+2}-1)}{5^{n}+8^{n}} =\lim\dfrac{4.8^{n}-9.6^{n}-2^{n}}{5^{n}+8^{n}} =\lim\dfrac{4-9.(\dfrac{6}{8})^{n}-(\dfrac{2}{8})^{n}}{(\dfrac{5}{8})^{n}+1} =\lim\dfrac{4-9.0-0}{0+1} =4\)