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Possible Duplicate:
Why is $1^{\infty}$ considered to be an indeterminate form

this is probably a very simple question for analysts, but i don't understand why the limit of the function $ \lim_{n \to \infty}1^n$ does not exist.

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    It is defined. This isn't what people mean when they say that $1^{\infty}$ is an indeterminate form.2011-08-05
  • 4
    Just to be clear: The term $1^n = 1$ for all $n$. So, $\displaystyle\lim_{n \to \infty} 1^n = 1$. However, if $\displaystyle\lim_{n \to \infty} f(n) = 1$ and $\displaystyle\lim_{n \to \infty} g(n) = \infty$, then $\displaystyle\lim_{n \to \infty} f(n) ^{g(n)}$ is indeterminant. This last fact is discussed at length in the link above.2011-08-05

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