求解一道数学题目~~`

来源：百度知道 编辑：UC知道 时间：2024/05/03 06:52:43
求解一道数学题目,题目是:
1/1*3(1乘3分之1)+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8
加起来等于多少,要简便的方法~~

1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8
=(1-1/3)*1/2+(1/2-1/4)*1/2+(1/3-1/5)*1/2+(1/4-1/6)*1/2+(1/5-1/7)*1/2+(1/6-1/8)*1/2
=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8)
=1/2*(1+1/2-1/7-1/8)
=69/112

通分啊

1/1*3(1乘3分之1)+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8
=1/2(1-1/3)+1/2(1/2-1/4)+1/2(1/3-1/5)+1/2(1/4-1/6)+1/2(1/5-1/7)+1/2(1/6-1/8)
=1/2(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8)
=1/2(1+1/2-1/7-1/8)
=69/112

原式=(1/1*3+1/3*5+1/5*7)+(1/2*4+1/4*6+1/6*8)
=1/2[(1-1/3+1/3-1/5+1/5-1/7)+(1-1/3-1/4+1/4-1/6+1/6-1/8)]
=1/2[(1-1/7)+(1/2-1/8)]
=1/2(6/7+3/8)
=1/2*69/56
=69/112

69/112

Sorry.I don't know~~