由规律可知：
1／(1+√2) +1／(√2+√3)+1／(√3+√4)+...+1／(√2009+√2010)+1／(√2010+√2011)
=(√2 -1)／[(1+√2)(√2 -1)] +(√3-√2)／[(√2+√3)(√3-√2)]+(√4-√3)／[(√3+√4)(√4-√3)]+...
+(√2010-√2009)／[(√2009+√2010)(√2010+√2009)]
+(√2011-√2010)／[(√2010+√2011)(√2011+√2010)]
=(√2 -1)+(√3-√2)+(√4-√3)+...+(√2010-√2009)+(√2011-√2010)
=(√2011) -1