用简便方法计算(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+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)

令a=1/2+1/3+1/4,b=1/2+1/3+1/4+1/5
b-a=1/5

原式＝(1+a)*b-(1+b)a=b+ab-a-ab=b-a=1/5