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

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

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

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

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

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

oiljdljdio - 魔法师 五级 是对的

1-3+5-7+... (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简算(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简便计算 1/1*3+1/1*3*5+1/1*3*5*7+1/1*3*5*7*9-73/945 (1/3+1/5+1/7)*(1/5+1/7+1/9)-(1/3+1/5+1/7+1/9)*(1/5+1/7)=? 1/3+1/5+1/7+.+1/2n+1 1/1*3*5+1/3*5*7+1/5*7*9.+1/95*97*99 1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013 简算:1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19= 计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21) 1/1×3+1/3×5+1/5×7+1/7×9+.+1/2013×2015 1/1*3+1/3*5+1/5*7+1/7*9+.+1/101*103 帮帮忙1/1*3+1/3*5+1/5*7+1/7*9+...1/99*101 1/1*3+1/3*5+1/5*7+1/7*9+1/49*51= 计算：1/1×3+1/3×5+1/5×7+1/7×9``````+1/2001×2003 (1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1 1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 (1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1