Szczegółowe wyjaśnienie:
[tex]\lim\limits_{n\to\infty}\left(1-\dfrac{1}{3n+5}\right)^{2n-1}=\lim\limits_{n\to\infty}\left(1+\dfrac{1}{-3n-5}\right)^{2n-1}\\\\=\lim\limits_{n\to\infty}\bigg[\left(1+\dfrac{1}{-3n-5}\right)^{-3n-5}\bigg]^{\dfrac{2n-1}{-3n-5}}=e^{\lim\limits_{n\to\infty}\left(\dfrac{2n-1}{-3n-5}\right)}\\\\=e^{\lim\limits_{n\to\infty}\left(\dfrac{n\left(2-\frac{1}{n}\right)}{n\left(-3-\frac{5}{n}\right)}\right)}=e^{\lim\limits_{n\to\infty}\left(\dfrac{2-\frac{1}{n}}{-3-\frac{5}{n}}\right)}=e^{-\frac{2}{3}}[/tex]
[tex]\left(1+\dfrac{1}{n}\right)^n\xrightarrow{n\to\infty}e[/tex]