解
1/(1*2)+1/(2*3)+1/(3*4)+...+1/(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)+……+(1/2012-1/2012)-1/2013——内部抵消
=1-1/2013
=2012/2013
裂项
1/n(n+1)=1/n-1/(n+1)能解释一下吗？1/(1*2)=1-1/21/(2*3)=1/2-1/3………………都是通过这个式子裂项的1/n(n+1)=1/n-1/(n+1)这个式子要记住以后遇到这种题可以用不懂追问