Question

18．計(jì)算|1-$\sqrt{2}$|+|$\sqrt{2}$-$\sqrt{3}$|+|$\sqrt{3}$-2|+|2-$\sqrt{5}$|+…+|$\sqrt{2013}$-$\sqrt{2014}$|的結(jié)果是（　�。�

• A． $\sqrt{2013}$-1
• B． $\sqrt{2014}$-1
• C． 1-$\sqrt{2013}$
• D． 1-$\sqrt{2014}$

Answer 1

分析 利用絕對(duì)值的性質(zhì)分別化簡(jiǎn)各式進(jìn)而合并求出即可．

解答 解：|1-$\sqrt{2}$|+|$\sqrt{2}$-$\sqrt{3}$|+|$\sqrt{3}$-2|+|2-$\sqrt{5}$|+…+|$\sqrt{2013}$-$\sqrt{2014}$|
=$\sqrt{2}$-1+$\sqrt{3}$-$\sqrt{2}$+2-$\sqrt{3}$+$\sqrt{5}$-2+…+$\sqrt{2014}$-$\sqrt{2013}$
=-1+$\sqrt{2014}$．
故選：B．

點(diǎn)評(píng) 此題主要考查了二次根式的加減以及絕對(duì)值的性質(zhì)，正確去絕對(duì)值是解題關(guān)鍵．