1/6+1/12+1/20+1/30．．．．．+1/2005*2006
=1/(2*3)+1/(3*4)+...+1/(2005*2006)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/2005-1/2006)
=1/2-1/2006
=自己化简~:)