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walker242
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Homework Statement
Calculate the limit of [tex]a_{n} = \frac{n^n}{(n-1)^n}[/tex] when [tex]n\rightarrow \infty[/tex], where n is an integer.
Homework Equations
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The Attempt at a Solution
[tex]a_{n} = \frac{n^n}{(n-1)^n} = \left(\frac{n}{n-1}\right)^{n} = e^{\ln\frac{n}{n-1}\right)^{n}} = e^{n\ln\frac{n}{n-1}} = e^{n\left(\ln(n)-\ln(n-1)\right)} = e^{-n\left(\ln(n-1)-\ln(n)\right)} = e^{-n\left(\ln\frac{n-1}{n}\right)} = e^{-n\left(\ln\left(1-\frac{1}{n}\right)\right)} = [/tex]que?