(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2011*1/2012)
=-【(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2011-1/2012)】
=-(1-1/2012)
=-2011/2012
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2011*1/2012)
=-【(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2011-1/2012)】
=-(1-1/2012)
=-2011/2012