1/(√2+1)+……+1/(√2012+√2011)
=(√2-1)/[(√2+1)(√2-1)]+(√3-√2)/[(√3+√2)(√3-√2)]+……+(√2012-√2011)/[(√2012+√2011)(√2012-√2011)]
=(√2-1)+(√3-√2)+……+(√2012-√2011)
=√2012-1

看题目应该是还要乘以√2012+1吧,
原式=(√2012-1)(√2012+1）
=2012-1=2011

中间多次用到平方差公式~