(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1
7个回答

方法一

设a=1/2+1/3+1/4;

则原式化简为(1+a)*(a+1/5)-(1+a+1/5)*a

=(a+1/5+a平方+1/5a)-(a+a平方+1/5a)

=1/5

方法二

设1+1/2+1/3+1/4=a,1/2+1/3+1/4=b,则a-b=1.

原式=a×(b+1/5)-(a+1/5)×b

=ab+1/5a-ab-1/5b

=1/5(a-b)

=1/5×1

=1/5

方法三

(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)

=(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4+1/5) -(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)-(1/2+1/3+1/4)=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)=1/5