Question

1/1*3+1/3*5+1/5*7+...+1/2007*2009=?

Answer 1

1/1*3=（1-1/3）*0.5
1/3*5=（1/3-1/5）*0.5
......
那么1/1*3+1/3*5+1/5*7+1/7*9+19*11+........+1/1995*1997+1/1997*1999
=（（1-1/3）+（1/3-1/5）+（1/5-1/9）+...+（1/2007-1/2009））*0.5=（1-1/2009）*0.5=1004/2009

Answer 2

=0.5*(1-1/3+1/3-1/5+.....1/2005-1/2007+1/2007-1/2009)=0.5*(1-1/2009)=1004/2009

Answer 3

=1/2*(1/1-1/3+1/3-1/5+1/5-1/7+...+1/2007-1/2009)
=1/2*(1/1-1/2009)=1004/2009

Answer 4

1/1*3+1/3*5+1/5*7+...+1/2007*2009
=1/2*(1-1/3+1/3-1/5+1/5-1/7+......+1/2007-1/2009)
=1/2*(1-1/2009)
=1004/2009

Answer 5

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