|1-根号2|+|根号2-根号3|+|根号3-根号4|+|根号4-根号5|+.+|根号2012-根号2013|(结果保留根号)

问题描述:

|1-根号2|+|根号2-根号3|+|根号3-根号4|+|根号4-根号5|+.+|根号2012-根号2013|(结果保留根号)

=根号(2013)-1

(根号2013)-1
原式=√2-1+√3-√2+√4-√3+。。。。+√2012-√2011+√2013-√2012
=√2013-1
求采纳,谢谢、

|1-根号2|+|根号2-根号3|+|根号3-根号4|+|根号4-根号5|+.+|根号2012-根号2013|
=-1+根号2-根号2+根号3-根号3+根号4-...-根号2012+根号2013
=根号2013-1