计算:1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+...+1/(2003+2005+2007)=?
问题描述：
计算:1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+...+1/(2003+2005+2007)=?
答
通项是1/(2n-1)(2n+1)(2n+3)=1/4[1/(2n-1)(2n+1)-1/(2n+1)(2n+3)],于是原式就变成了1/4（1/3-1/15+1/15-1/35……+1/2003*2005-1/2005*2007）=1/4（1/3-1/2005*2007）,后面的就不用我算了吧.