现有11个单位分式,见下方一、1/x+1,1/x+2,1/x+3,1/x+4,1/x+5,1/x（x+1）,1/(x+1)(x+2),1/(x+2)(x+3),1/(x+3)(x+4),1/(x+4)(x+5),1/(x+5)(x+6).请你从中挑选出5个,填上正负号,使他们的和等于-1/x+5.写出探究过程二、请你从

Question

现有11个单位分式,见下方
一、1/x+1,1/x+2,1/x+3,1/x+4,1/x+5,1/x（x+1）,1/(x+1)(x+2),1/(x+2)(x+3),
1/(x+3)(x+4),1/(x+4)(x+5),1/(x+5)(x+6).请你从中挑选出5个,填上正负号,使他们的和等于-1/x+5.写出探究过程
二、请你从1/2,1/3,1/4…,1/45,1/46这45个单位分数中挑选7个,添上正负号,使他们的和等于1,写出探究过程.
急!答得好、快,有加分!

Answer 1

-1/(x+1)+1/(x+1)(x+2)-1/(x+2)(x+3)+1/(x+3)(x+4)-1/(x+4)(x+5)
=-1/(x+1)+1/(x+1)+1/(x+2)-1/(x+2)-1/(x+3)+1/(x+3)+1/(x+4)-1/(x+4)-1/(x+5)
=1/(x+1)-1/(x+1)+1/(x+2)-1/(x+2)+1/(x+3)-1/(x+3)+1/(x+4)-1/(x+4)-1/(x+5)
=-1/(x+5)
1/2+1/6+1/12+1/20+1/30+1/42+1/7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7
=1