1/2+1/6+1/12+1/20+1/1/30+1/42+……+1/(2006x2007)

来源：百度知道 编辑：UC知道 时间：2024/05/25 05:22:31
"1/?" 代表?分之1 最后一个是2006乘以2007分之1
要简单过程
大家快来哇
那个1/1/30打错了,就是1/30

1/2+1/6+1/12+1/20+1/1/30+1/42+……+1/(2006x2007)=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+......+1/(2006x2007)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+......+1/2006-1/2007=1-1/2007=2006/2007

=1-1/2+1/2-1/3+1/3-1/4+ ^^^^^^ ＋1/2006-1/2007=2006/2007

1/2+1/6+1/12+1/20+1/1/30+1/42+……+1/(2006x2007)
＝1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+……+1/(2006x2007)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+（1/5-1/6）＋（1/64-1/7）……+(1/2006-1/2007)
＝1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6＋1/6-1/7……+1/2006-1/2007
＝1-1/2007
＝2006/2007

1/2=1-1/2,1/6=1/2-1/3,1/12=1/3=1/4,.....1/(2006*2007)=1/2006-1/2007
所以,1/2+1/6+1/12+1/20+1/30+1/42+……+1/(2006x2007)=1-1/2+1/2-1/3+1/3-1/4+....＋1/2006-1/2007=2006/2007