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=?

1/1*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...

全部展开

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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