1/1*3-1/3*5-1/5*7-.-1/2005*2007

问题描述:

1/1*3-1/3*5-1/5*7-.-1/2005*2007

=1/2[(1-1/3)-(1/3-1/5)-(1/5-1/7)-(1/7-1/9).-(1/2005-1/2007)]
=1/2[1-2/3+1/5-1/5+1/7-1/7.+1/2007]
=1/2(1/3+1/2007)