1/1*3+1/2*4+1/3*5+...+1/2005*2007

问题描述:

1/1*3+1/2*4+1/3*5+...+1/2005*2007

题目是1/(1*3)+1/(2*4)+...
因为1/(1*3)=1/2*(1/1-1/3)
所以原式=1/2*(1/1-1/3)+1/2*(1/2-1/4)+1/2*(1/3-1/5)+1/2*(1/4-1/6)+...
=1/2*(1/1+1/2-1/2006-1/2007)