题目
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)
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)
提问时间:2020-08-03
答案
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
=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
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