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Compute the following limit:

$\lim_{n\to\infty} \{ (\sqrt2+1)^{2n} \}$ where $\{x\}$ is the fractional part of $x$. I need some hints here. Thanks.

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    I think $\{(\sqrt2+1)^{2n}\}=2^n\sqrt2$2012-06-22

1 Answers 1

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Consider $ (\sqrt2+1)^{2n} + (\sqrt2-1)^{2n} $

Try to show that it is an integer and hence this fractional part you are looking for is $1 - (\sqrt2-1)^{2n}$ Now the limit becomes easy.

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    okay!, i got your point :).Thanks!!2012-06-22