|1-根号2|+|根号2-根号3|+……+|根号2011-根号2012|等于多少

问题描述:

|1-根号2|+|根号2-根号3|+……+|根号2011-根号2012|等于多少

|1-根号2|+|根号2-根号3|+……+|根号2011-根号2012|
=√2-1+√2-√3+……+√2012-√2011
中间的都被消去
=√2012-1
=2√503-1