令a=1/2+1/3+1/4
则1+1/2+1/3+1/4=1+a
1/2+1/3+1/4+1/5=a+1/5
1+1/2+1/3+1/4+1/5=1+a+1/5
所以原式=(1+a)(a+1/5)-a(1+a+1/5)
=a(1+a)+1/5*(a+1)-a(1+a)-a*1/5
=1/5*a+1/5-1/5*a
=1/5
一道奥数题,急救!（1+1/2+1/3+1/4）×（1/2+1/3+1/4+1/5）-（1+1/2+1/3+1/4+1/
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