Bài tập 3 trang 75 SBT Toán 11 Tập 1 Chân trời sáng tạo - CTST

a) Ta có: $\text{lim}{\left(\frac{\sqrt{3}}{2}\right)}^n=0.$

b) Ta có: $\text{lim}\frac{3^n}{4^n-1}=\text{lim}\frac{{\left(\frac{3}{4}\right)}^n}{1-{\left(\frac{1}{4}\right)}^n}=\frac{\text{lim}{\left(\frac{3}{4}\right)}^n}{1-\text{lim}{\left(\frac{1}{4}\right)}^n}=\frac{0}{1-0}=0.$

c) Ta có: $\text{lim}\frac{3^n-2^n}{3^n+2^n}=\text{lim}\frac{1-{\left(\frac{2}{3}\right)}^n}{1+{\left(\frac{2}{3}\right)}^n}=\frac{1-\text{lim}{\left(\frac{2}{3}\right)}^n}{1+\text{lim}{\left(\frac{2}{3}\right)}^n}=\frac{1-0}{1+0}=1.$

d) Ta có: $\text{lim}\frac{4^{n+1}}{3^n+4^n}=\text{lim}\frac{4}{{\left(\frac{3}{4}\right)}^n+1}=\frac{4}{\text{lim}{\left(\frac{3}{4}\right)}^n+1}=\frac{4}{0+1}=4$.

-- Mod Toán 11 HỌC247