用简便方法算:丨1/3-1/2丨+丨1/4-1/3丨+丨1/5-1/4丨+...+丨1/2008-1/2007丨谢.狠急的

Question

用简便方法算:丨1/3-1/2丨+丨1/4-1/3丨+丨1/5-1/4丨+...+丨1/2008-1/2007丨 谢.
狠急的

Answer 1

由题意可知,每个绝对值符号内均为负数,而负数的绝对值等于其相反数.
所以,丨1/3-1/2丨+丨1/4-1/3丨+丨1/5-1/4丨+...+丨1/2008-1/2007丨
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+…+(1/2007-1/2008)
=1/2-1/3+1/3-1/4+1/4-1/5+…+1/2007-1/2008
=1/2-1/2008
=1003/2008