4x/1x2+4x/2x3+4x/4x5+4x/5x6+.+4x/2010x2011+4x/2011x2012=1

问题描述:

4x/1x2+4x/2x3+4x/4x5+4x/5x6+.+4x/2010x2011+4x/2011x2012=1

4x(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2011-1/2012)=1
4x(1-1/2012)=1
4x(2011/2012)=1
2011x/503=1
x=503/2011