【微分積分】1-1-3 等比数列の極限｜問題集

\(\displaystyle =\lim_{n\to\infty}\frac{3}{(\frac{2}{3})^n+1}\)
\(=3\)

\(\displaystyle =\lim_{n\to\infty}\frac{3^n(1+\frac{2}{3^n})}{2^n(1+\frac{1}{2^n})}\)
\(\displaystyle =\lim_{n\to\infty}\left(\frac{3}{2}\right)^n\frac{1+\frac{2}{3^n}}{1+\frac{1}{2^n}}\)
\(=\infty\)

\(\displaystyle =\lim_{n\to\infty}\frac{4^n+3^n}{4^{n+1}+2^{n+1}}\)
\(\displaystyle =\lim_{n\to\infty}\frac{1+(\frac{3}{4})^n}{4+2(\frac{1}{2})^n}\)
\(\displaystyle =\frac{1}{4}\)