1/1*3+1/3*5+1/5*7+.1/2005*2007=?

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1/1*3+1/3*5+1/5*7+.1/2005*2007=?
1/1*3+1/3*5+1/5*7+.1/2005*2007=?

1/1*3+1/3*5+1/5*7+.1/2005*2007=?
1/1*3+1/3*5+1/5*7+...1/2005*2007
=(2/1*3+2/3*5+2/5*7+...+2/2005*2007)/2
因2/n*(n+2)=(n+2-n)/n(n+2)=1/n-1/(n+2)
所以
1/1*3+1/3*5+1/5*7+...1/2005*2007
=(1/1-1/3+1/3-1/5+...+1/2005-1/2007)/2
=1003/2007

1/1*3+1/3*5+1/5*7+........1/2005*2007
=(1-1/3+1/3-1/5+1/5-1/7+----+1/2005-1/2007)/2
=(1-1/2007)/2
=1003/2007

0.5x(1/1-1/3)+0.5x(1/3-1/5)+0.5x(1/5-1/7)+……+0.5x(1/2005-1/2007)=0.5(1/1-1/3+1/3-1/5+1/5-……+1/2005-1/2007)=0.5x(1/1-1/2007)=0.5*2006/2007=1003/2007

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+.+1/2n+1 (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 1 1 1 1 3 5 7 1 5 13 25 1 7 25 why 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