1/1*3+1/3*5+1/5*7+...+1/2007+2009说出那样做的原因哦

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 11:52:30
1/1*3+1/3*5+1/5*7+...+1/2007+2009说出那样做的原因哦

1/1*3+1/3*5+1/5*7+...+1/2007+2009说出那样做的原因哦
1/1*3+1/3*5+1/5*7+...+1/2007+2009
说出那样做的原因哦

1/1*3+1/3*5+1/5*7+...+1/2007+2009说出那样做的原因哦
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+.+1/2005-1/2007+1/2007-1/2009)
=1/2(1-1/2009)=1004/2009

最后一个错了，应该是1/2007*2009
1/1*3=1/2*(1-1/3)
1/3/5=1/2*(1/3-1/5)
后面以此类推
所以原式=1/2*(1-1/3+1/3-1/5+……+1/2007-1/2009)
=1/2*(1-1/2009)
=1004/2009

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

1/3=(1/2)(1-1/3)
1/15=(1/2)(1/3-1/5)
1/3+1/15=(1/2)(1-1/3+1/3-1/15)
.......
原式=(1/2)(1-1/2009)=1004/2009

1/1*3+1/3*5+1/5*7+...+1/2007*2009(应该是乘号吧)
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*(1-1/2009)
=1/2*2008/2009
=1004/2009

1/n(n+2)=1/2*[1/n-1/(n+2)]
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*(1-1/2009)
=1/2*2008/2009
=1004/2009

1/n*(n+2)=1/2*(1/n-1/(n+2))
于是原式=1/2*(1-1/3+1/3-1/5+...+1/2007-1/2009)=(1/2)*2008/2009=1004/2009

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