计算1/1*3+1/3*5+...+1/2009*2011+1/2011*2013

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计算1/1*3+1/3*5+...+1/2009*2011+1/2011*2013
计算1/1*3+1/3*5+...+1/2009*2011+1/2011*2013

计算1/1*3+1/3*5+...+1/2009*2011+1/2011*2013
1/1*3+1/3*5+...+1/2009*2011+1/2011*2013=
(1/2)*(1-1/3)+(1/2)*(1\3-1\5).+(1/2)*(1/2009-1/2011)+(1\2)*(1/2011-1/2013)=
(1/2)*(1-1/3+1/3-1/5.+1/2009-1/2011+1/2011-1/2013)=
(1/2)*(1-1/2013)=(1/2)*(2012/2013)=1006/2013

望采纳!

=1/2(2/1*3+2/3*5+...+2/2009*2011+2/2011*2013)
=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/2011-1/2013)
=1/2(1-1/2013)
=1006/2013

1006/2013