Question

$L= \lim_{n \to \infty} \frac{n^{n}}{(n+1)^{n}}$

Answer 1

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The solution is in the image.


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Purva
Global Brainly Community

Answer 2

$\lim _{n\to \infty \:}\left(\frac{n^n}{\left(n+1\right)^n}\right) \\ \frac{n^n}{\left(n+1\right)^n}=\left(\frac{n}{\left(n+1\right)}\right)^n \\ =\lim _{n\to \infty \:}\left(\left(\frac{n}{n+1}\right)^n\right) \\\lim _{n\to \infty }\left(\left(\frac{n}{n+k}\right)^n\right)=\frac{1}{e^k} =\frac{1}{e^1}=\frac{1}{e}$