Granica

[Artegor]

Oblicz granicę ciągu

\(u_n=(1+ \frac{4}{n})^n\)

[Arni123]

\((1+ \frac{4}{n})^n=\left(1+ \frac{1}{\frac{n}{4}}\right)^n=\left[\left(1+ \frac{1}{\frac{n}{4}}\right)^{\frac{n}{4}}\right]^4 \to e^4 (n \to \infty)\)

[eresh]

\(\Lim_{n\to\infty}\left(1+\frac{4}{n}\right)^n=\Lim_{n\to\infty} \left[ \left( 1+\frac{4}{n}\right)^{\frac{n}{4}} \right] ^4=e^4\)