我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005

问题描述:

我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005

1/1x3+1/3x5+1/5x7+.1/2003x2005
=(1/2)(1-1/3)+(1/2)(1/3-1/5)+………………+(1/2)(1/2003-1/2005)
=(1/2)*[1-1/3+1/3-1/5+…………+1/2003-1/2005]
=(1/2)*(1-1/2005)
=(1/2)*(2004/2005)
=1002/2005