若1/2+1/6+1/12+.+1/x（x+1）=2013/2014,则x=?
问题描述：
若1/2+1/6+1/12+.+1/x（x+1）=2013/2014,则x=?
答
由于1/[x(x+1)]=1/x-1/(x+1)
所以，1/2+1/6+1/12+...+1/x(x+1)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+1/x-1/(x+1)
=1-1/(x+1)
既然1-1/(x+1)=2013/2014，那么,x=2013
完毕
答
1/2+1/6+1/12+....+1/x（x+1）=2013/2014
1/1x2+1/2x3+1/3x4+……+1/x(x+1)=2013/2014
1-1/2+1/2-1/3+1/3-1/4+……+1/x-1/(x+1)=2013/2014
1-1/(x+1)=1-1/2014
x+1=2014
x=2013
答
1/1×2+1/2×3+1/3×4+.+1/x（x+1）=2013/2014
1-1/2+1/2-1/3+1/3-1/4+……++1/x-1/（x+1）=2013/2014
1-1/(x+1)=2013/2014
1/(x+1)=1/2014
x+1=2014
x=2013