简便计算(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

Answer 1

令a=1/2+1/3+1/4,b=1/2+1/3+1/4+1/5

(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1+a)*b-(1+b)*a
=b+ab-a-ab
=b-a
=1/5