limit

[lampat]

\(\displaystyle \lim_{n\rightarrow \infty}\left\{\left(\sqrt{2}+1\right)^n\right\}=\)

Where \(\displaystyle \left\{x\right\} = \) fractional part and \(\displaystyle n\in\mathbb{N}\)

 

[pka]

\(\displaystyle \lim_{n\rightarrow \infty}\left\{\left(\sqrt{2}+1\right)^n\right\}=\)
Where \(\displaystyle \left\{x\right\} = \) fractional part and \(\displaystyle n\in\mathbb{N}\)

Look at this webpage.
You will see that the fractional parts function has the following property:
\(\displaystyle \forall n\in\mathbb{Z}\) we have \(\displaystyle \{x+n\}=\{x\}\)