1/(13)+1/(35)+1/(57)……+1/(20012003)

来源：百度知道编辑：UC知道时间：2024/06/22 21:14:02

用简便方法计算．

拆项
1/(3*5)=1/2*(1/3-1/5).....
最后的结果是
1/2*(1/3-1/2003)=...自己算一下

1/2(1/1-1/3+1/3-1/5+.....+1/2001-1/2003)=1/2(1-1/2003}=1001/2003

1/2[（1-1/3）+（1/3-1/5）+（1/5-1/7）+.....+（1/2001-1/2003）]
=1/2[1-1/2003]=1001/2003

告诉你解题思路
1/(1*3)+1/(3*5)+1/(5*7)……+1/(2001*2003)
=〔2/（1*3）+2/（3*5）+2/（5*7）……+2/（2001*2003）〕/2
=〔（1/1-1/3）+（1/3-1/5）+……（1/2001-1/2003）〕/2
=（1/1-1/3+1/3-1/5+……+1/2001-1/2003）/2
=（1/1-1/2003）/2
=2002/2003/2
=1001/2003

=1/2*[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/2001-1/2003)]
=1/2*[1-1/2003]
=1/2*(2002/2003)
=1001/2003

1/(1*3)+1/(3*5)+1/(5*7)……+1/(2001*2003)
=〔2/（1*3）+2/（3*5）+2/（5*7）……+2/（2001*2003）〕/2
=〔（1/1-1/3）+（1/3-1/5）+……（1/2001-1/2003）〕/2
=（1/1-1/3+1/3-1/5+……+1/2001-1/2003）/2
=（1/1-1/2003）/2
=2002/2003/2
=1001/2003

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) (1-1/100)(1-1/99)(1-1/98)......(1-1/3 (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) 1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/2+1+1/3+1+1/4+......+1/100=? 1+1/2+1/3+.....+1/n 1+1/2+1/3+...+1/100 1+1/3+1/6+........+1/55 1-1/2+1/3-.....-1/10