作业帮(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)怎么做,求讲解
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/28 10:49:10
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)怎么做,求讲解
(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)求讲解!
(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)求讲解!
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
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