Bài tập 3 trang 130 SGK Toán 11 NC

a) Ta có \(\left| {0,99} \right| < 1 \Rightarrow \lim {u_n} = \lim {\left( {0,99} \right)^n} = 0\)

b) Ta có \(\left| {{u_n}} \right| = \left| {\frac{{{{\left( { - 1} \right)}^n}}}{{{2^n} + 1}}} \right| = \frac{1}{{{2^n} + 1}} < {\left( {\frac{1}{2}} \right)^n}\)

và \(\lim {\left( {\frac{1}{2}} \right)^n} = 0 \Rightarrow \lim {u_n} = 0\)

c) Ta có

\(\begin{array}{l}
\left| {{u_n}} \right| = \left| { - \frac{{\sin \frac{{n\pi }}{5}}}{{{{\left( {1,01} \right)}^n}}}} \right| = \frac{{\left| {\sin \frac{{n\pi }}{5}} \right|}}{{{{\left( {1,01} \right)}^n}}} \le {\left( {\frac{1}{{1,01}}} \right)^n},\\
\lim {\left( {\frac{1}{{1,01}}} \right)^n} = 0 \Rightarrow \lim {u_n} = 0
\end{array}\)

-- Mod Toán 11 HỌC247