计算1/(1+√2)+1/(√2+√3)+.+1/(√2010+√2011)
问题描述：
计算1/(1+√2)+1/(√2+√3)+.+1/(√2010+√2011)
√是根号
答
=1(1-√2)/(1+√2)(1-√2)+1(√2-√3)/(√2+√3)(√2-√3)+.+1(√2010-√2011)/(√2010+√2011)(√2010-√2011)
=1(1-√2)/(-1)+1(√2-√3)/(-1)+.+1(√2010-√2011)/(-1)
=(-1+√2)+(-√2+√3)+.+(-√2010+√2011)
=-1+√2011
你可以列在草稿纸上看下