谁知1/(1*4)-1/(4*7)-1/(7*10)-1/(10*13)......-1/(2002*2005)-1/(2005*2008)

问题描述:

谁知1/(1*4)-1/(4*7)-1/(7*10)-1/(10*13)......-1/(2002*2005)-1/(2005*2008)

(1/3)*(1-1/4+1/4-1/7+1/7-1/10+1/10.+1/2005-1/2008
=(1/3)*(1-1/2008)
=1/3*2007/2008
=669/2008