Question

19．計(jì)算：|$\frac{1}{2}-1$|+|$\frac{1}{3}-\frac{1}{2}$|+|$\frac{1}{4}$-$\frac{1}{3}$|+…+|$\frac{1}{2016}$-$\frac{1}{2015}$|

Answer 1

分析 根據(jù)絕對(duì)值的定義化簡(jiǎn)，再利用有理數(shù)的加減法計(jì)算即可．

解答 解：|$\frac{1}{2}-1$|+|$\frac{1}{3}-\frac{1}{2}$|+|$\frac{1}{4}$-$\frac{1}{3}$|+…+|$\frac{1}{2016}$-$\frac{1}{2015}$|
=$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{2015}-\frac{1}{2016}$
=1-$\frac{1}{2016}$
=$\frac{2015}{2016}$．

點(diǎn)評(píng) 此題考查有理數(shù)的加減混合計(jì)算，關(guān)鍵是根據(jù)絕對(duì)值的定義化簡(jiǎn)．