|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|这题如何解啊.注:1/2表示二分之一.

问题描述:

|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|这题如何解啊.注:1/2表示二分之一.

|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/2011-1/2012
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+.+(-1/2011)1/2011)-1/2012
=1+0+0+0+0+.+0-1/2012
=1-1/2012
=2011/2012