Question

Answer 1

1A;2B;3B;4B;5B;6D

Answer 2

1. \(\lim\dfrac{1}{n^k}=0\)

2. \(\lim\dfrac{3^n-2.5^n}{3.5^n+2.4^n}=\lim\dfrac{\left(\dfrac{3}{5}\right)^n-2}{3+2\left(\dfrac{4}{5}\right)^n}=-\dfrac{2}{3}\)

3. \(\lim\dfrac{4n-2021}{2022+6n}=\lim\dfrac{4-\dfrac{2021}{n}}{\dfrac{2022}{n}+6}=\dfrac{4}{6}=\dfrac{2}{3}\)

4. \(\lim\limits_{x\rightarrow0}\left(x^3-3x+1\right)=0^3-3.0+1=1\)

5. Tổng đã cho là tổng cấp số nhân lùi vô hạn với \(u_1=-\dfrac{1}{5};q=-\dfrac{1}{5}\)

\(\Rightarrow S=\dfrac{u_1}{1-q}=\dfrac{-\dfrac{1}{5}}{1+\dfrac{1}{5}}=-\dfrac{1}{6}\)