1/1×2 + 1/2×3 + 1/3×4 +…+1/2013×2014 + 1/2014×2015=1-1/2+1/2-1/3+1/3-1/4......+1/2013-1/2014+1/2014-1/2015=1-1/2015=2014/2015
