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-√2...