求简便运算1.2又6209/10013*10693/22869÷33337/106022.(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)3.1/(1*2)+1/(2*3)+1/(3*4)+...+1/(999*1000)4.1+1/(1*2)+1/(1+2+3)+...+1/(1+2+3+...+20)5.1/(1

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求简便运算1.2又6209/10013*10693/22869÷33337/106022.(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)3

求简便运算1.2又6209/10013*10693/22869÷33337/106022.(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)3.1/(1*2)+1/(2*3)+1/(3*4)+...+1/(999*1000)4.1+1/(1*2)+1/(1+2+3)+...+1/(1+2+3+...+20)5.1/(1
求简便运算
1.2又6209/10013*10693/22869÷33337/10602
2.(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)
3.1/(1*2)+1/(2*3)+1/(3*4)+...+1/(999*1000)
4.1+1/(1*2)+1/(1+2+3)+...+1/(1+2+3+...+20)
5.1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(98*99*100)

求简便运算1.2又6209/10013*10693/22869÷33337/106022.(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)3.1/(1*2)+1/(2*3)+1/(3*4)+...+1/(999*1000)4.1+1/(1*2)+1/(1+2+3)+...+1/(1+2+3+...+20)5.1/(1
3.1/(1*2)+1/(2*3)+1/(3*4)+...+1/(999*1000)
=1-1/2+1/2-1/3+...+1/999-1/1000
=1-1/1000=999/1000
4.1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+20)
=1+2/(2*3)+2/(3*4)+2/(4*5)+...+2/(20*21)
=1+2*(1/2-1/3+1/3-1/4+...+1/20-1/21)
=1+2*(1/2-1/21)
=40/21
5.1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(98*99*100)
=(1/2)*[1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+...+1/(98*99)-1/(99*100)]
=(1/2)*[1/2-1/9900}
=4949/19800

3.裂项得,原式=1-1/2+1/2-1/3+…+1/999-1/1000=1-1/1000=999/1000
4.原式=2/(1*2)+2/(2*3)+…+2/(20*21)=2*[1/(1*2)+1/(2*3)+…+1/(20*21)]=
接下来与3同理

2.观察哈,正的相加,负的相加,可得26*(1/28-1/30)
3.是裂项相消,1/(2*3)=1/2-1/3
4.通向可表示为an=2/(n(n-1)),然后就跟题3一样了
5.1/((n-1)n(n+1))=1/2*(1/(n-1)n-1/n(n+1)),之后的话又跟第三题一样了……呵呵
第一题,我只会计算器……呵呵33/70

1.2+6209/10013*10693/22869*10602/33337
=自己算吧
2.1/2-1/3+1/4-1/5+1/7-1/10+1/14-1/15+1/28-1/30
=接下来自己算
三到五不会