(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)…+(-1/2012*1/2013)
=(1/2-1)+(1/3-1/2)+(1/4-1/3).+(1/2013-1/2012)
=-1+1/2-1/2+1/3-1/3+1/4-1/4.-1/2012+1/2013
=-1+1/2013
=-2012/2013
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)…+(-1/2012*1/2013)
=(1/2-1)+(1/3-1/2)+(1/4-1/3).+(1/2013-1/2012)
=-1+1/2-1/2+1/3-1/3+1/4-1/4.-1/2012+1/2013
=-1+1/2013
=-2012/2013