高校问答爱菲尔婚礼:一道小学的数学体,急待解决!~!~
来源：百度文库 编辑：高校问答 时间：2024/05/06 05:02:16
先观察:
1-1/2=1/1×2
1/2-1/3=1/2×3
1/3-1/4=1/3×4
1/4-1/5=1/4×5......
再用简便方法计算:
1/2+1/6+1/12+1/20+1/30
1-1/2=1/1×2
1/2-1/3=1/2×3
1/3-1/4=1/3×4
1/4-1/5=1/4×5......
再用简便方法计算:
1/2+1/6+1/12+1/20+1/30
1/2+1/6+1/12+1/20+1/30
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
方法为1/a(a+1)=1/a-1/(a+1)
所以
所求式子
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-(1/2-1/2)-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-1/6
=1-1/6
=5/6
原式=1/1*2+1/2*3+1/3*4+1/5*6=
（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+(1/5-1/6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6=1-1/6=5/6
1/2+1/6+1/12+1/20+1/30
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6=1-1/6=5/6
1/2+1/6+1/12+1/20+1/30
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6（减1个加1个就互相抵消了了）
=5/6