（1+1/2+1/3+1/4）*（1/2+1/3+1/4+1/6）—（1+1/2+1/3+1/4+

设 (1+1/2+1/3+1/4)=a (1/2+1/3+1/4)=b 则a-b=1 把a,b代入上面式子得
a(b+1/5)-(a+1/5)b
=ab+1/5a-ab-1/5b
=1/5(a-b)
=1/5追问

请问有简便计算么？

追答

这个已经够简便了

解：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+a)*1/5-a(1+a)-a*1/5
=(1+a)*1/5-a*1/5
=1/5+a*1/5-a*1/5
=1/5本回答被提问者采纳

设 (1+1/2+1/3+1/4)=a (1/2+1/3+1/4)=b 则a-b=1 把a,b代入上面式子得 a(b+1/5)-(a+1/5)b=ab+1/5a-ab-1/5b=1/5(a-b)=1/5 (上面的1/6打错,应该是1/5)