1/(√2+1)=(√2-1)/[(√2+1)(√2-1)]=(√2-1)/(2-1)=√2-11/(√3+√2)=(√3-√2)/[(√3-√2)(√3+√2)]=(√3-√2)/(3-2)=√3-√2……1/(√10+3)=(√10-3)/[(√10-3)(√10+3)]=(√10-3)/(10-9)=√10-3所以原式=(√2-1)+(√3-√2)+……+(√10-3)=√10-1
