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[lovemathforeverlqd]

Chứng minh rằng: $\lim_{n->\infty }(1+\frac{k}{n})^{n}=e^{k}$ 

Edited by lovemathforeverlqd, 11-11-2016 - 19:55.

[chanhquocnghiem]

Chứng minh rằng: $\lim_{n->\infty }(1+\frac{k}{n})^{n}=e^{k}$ 

$\lim_{n\to \infty}\left ( 1+\frac{k}{n} \right )^n=\lim_{n\to \infty}\left ( 1+\frac{1}{\frac{n}{k}} \right )^n=\lim_{n\to \infty}\left [ \left ( 1+\frac{1}{\frac{n}{k}} \right )^{\frac{n}{k}} \right ]^k=e^k$.