1\1*5+1\5*9+1\9*3+...+1\2009*2013
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![1\1*5+1\5*9+1\9*3+...+1\2009*2013](/uploads/image/z/755102-38-2.jpg?t=1%5C1%2A5%2B1%5C5%2A9%2B1%5C9%2A3%2B...%2B1%5C2009%2A2013)
1\1*5+1\5*9+1\9*3+...+1\2009*2013
1\1*5+1\5*9+1\9*3+...+1\2009*2013
1\1*5+1\5*9+1\9*3+...+1\2009*2013
1\1*5+1\5*9+1\9*3+...+1\2009*2013
=1/4*(1-1/5)+1/4*(1/5-1/9)+1/4*(1/9-1/13)+.1/4*(1/2009-1/2013)
=1/4*(1-1/5+1/5-1/9+1/9-1/13+.+1/2009-1/2013)
=1/4*(1-1/2013)
=1/4*2012/2013
=503/2013