(1-1/2^2)(1-1/3^2)(1-1/4^2).（1-1/2014^2）
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4).(1+1/2014)(1-1/2014)
=[(1+1/2)(1+1/3)(1+1/4).(1+1/2014)][(1-1/2)(1-1/3)(1-1/4).(1-1/2014)]
=[(3/2)(4/3)(5/4).(2015/2014)][(1/2)(2/3)(3/4).(2013/2014)]
=(2015/2)(1/2014)=2015/4028