(1/根号2+1)+(1/根号3+根号2)+(1/2+根号3)+(1/根号5+2)+……+(1/根号2010+根号2011)
问题描述:
(1/根号2+1)+(1/根号3+根号2)+(1/2+根号3)+(1/根号5+2)+……+(1/根号2010+根号2011)
答
1/(√2+1)+1/√(3+√2)+1/(2+√3)+1/(2+√5)+……+1/(√2010+√2011)
=√2-1+√3-√2+2-√3+√5-2+……+√2011-√2010
=(√2011)-1