( -1*1/2)+(-1/2*1/3)+(1/-3*1/4)+…+(-1/2012*1/2013)求过程
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( -1*1/2)+(-1/2*1/3)+(1/-3*1/4)+…+(-1/2012*1/2013)求过程
( -1*1/2)+(-1/2*1/3)+(1/-3*1/4)+…+(-1/2012*1/2013)求过程
( -1*1/2)+(-1/2*1/3)+(1/-3*1/4)+…+(-1/2012*1/2013)求过程
-1+1/2-1/2+1/3-1/3+1/4...-1/2012+1/2013
=-1+1/2013
=-2012/2013
-2012/2013
( -1*1/2)+(-1/2*1/3)+(1/-3*1/4)+…+(-1/2012*1/2013)
=-1+1/2-1/2+1/3-1/3+1/4...-1/2012+1/2013
=-1+1/2013
=-2012/2013
利用等式:1/N-1/(N+1)=1/N*1/(N+1)
原式=(1/2-1/1)+(1/3-1/2)+...+(1/2013-1/2012)=-1+1/2013=-2012/2013