lim((n-1)/n)^n,n->+inf)

calculator gives me e^-1 bt I don't know how.

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- Feb 5th 2009, 01:41 PMninano1205How to find this limit?
lim((n-1)/n)^n,n->+inf)

calculator gives me e^-1 bt I don't know how.

(Headbang) - Feb 5th 2009, 01:51 PMThePerfectHacker
Notice that $\displaystyle \tfrac{n-1}{n} = 1 - \tfrac{1}{n}$.

You should know that $\displaystyle \left( 1 + \tfrac{1}{n} \right)^n \to e$, in general $\displaystyle \left( 1+\tfrac{k}{n} \right)^n \to e^k$.

Therefore, $\displaystyle \left( 1 - \tfrac{1}{n} \right)^n \to e^{-1}$. - Feb 5th 2009, 02:07 PMninano1205calculus
Which part of calculus should I study if I don't know this?

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