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

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/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

1/1*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

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

1/1*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

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