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I was wondering if someone could help me figure out the asymptotic of $(1 + x)^{1/k}$, where $x$ is going to $0$ and $k$ is a fixed positive integer. I know it is going to 1, but I wanted to know the second term and the O-bound if possible.

Thank you for your help!

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up vote 1 down vote accepted

Hint: The Taylor polynomials will give you what you want.

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Thank you!! Greatly appreciated!! – J Kasahara Nov 9 '12 at 17:32

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