[1/（1+√2）+1/（√2+√3）+1/（√3+√4）+……+1/（√2001+√2002）+1/（√2002+√2003）]=(√2-1)/[(√2+1)(√2-1)]+(√3-√2)/[(√3+√2)(√3-√2)]+(√4-√3)/[(√4+√3)(√4-√3)]+...+(√2003-√2002)/[(√20...