1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 03:57:56
![1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008=?](/uploads/image/z/3860550-54-0.jpg?t=1%2F1%2A3%2B1%2F2%2A4%2B1%2F3%2A5%2B1%2F4%2A6%2B...%2B1%2F2005%2A2007%2B1%2F2006%2A2008%3D%3F)
1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008=?
1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008=?
1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008=?
=1/2(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/2005-1/2007+1/2006-1/2008)
=1/2(1+1/2-1/2007-1/2008)
后面化简的数值就太大了,不做了
1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008
=1/1*3+1/3*5++1/2005*2007...+1/2*4+1/4*6+.........+1/2006*2008
=1/2*(1-1/3)+1/2*(1/3-1/5)+..............+1/2*(1/2005-1/2007)+1/2*(1/2-1/4)+1...
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1/1*3+1/2*4+1/3*5+1/4*6+...+1/2005*2007+1/2006*2008
=1/1*3+1/3*5++1/2005*2007...+1/2*4+1/4*6+.........+1/2006*2008
=1/2*(1-1/3)+1/2*(1/3-1/5)+..............+1/2*(1/2005-1/2007)+1/2*(1/2-1/4)+1/2*(1/4-1/6)+..............+1/2*(1/2006-1/2008)
=1/2*(1-1/3+1/3-1/5+............+1/2005-1/2007)+1/2*(1/2-1/4+1/4-1/6+............+1/2006-1/2008)
=1/2*(1-1/2007)+1/2*(1/2-1/2008)
=1003/2007+1003/4016
=1003/2007+1003/4016
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