3、The first digit after the decimal point of $(1+\sqrt{2})^{2017}$ is

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3、The first digit after the decimal point of $(1+\sqrt{2})^{2017}$ is
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Analysis: We consider the conjugate $(\sqrt{2}-1)^{2017}$. It is easy to know that $(1+\sqrt{2})^{2017}+(1-\sqrt{2})^{2017} \in Z$, and $0<(\sqrt{2}-1)^{2017}<1$. Since $(\sqrt{2}-1)^{4}<0.5^{4}=0.0625$, it follows that $(\sqrt{2}-1)^{2017}<0.0625$, meaning the first digit after the decimal point of $(\sqrt{2}-1)^{2017}$ is 0, hence the first digit after the decimal point of $(\sqrt{2}+1)^{2017}$ is 0.