n^4+1/4
=(n^2+1/2)^2-n^2
=(n^2-n+1/2)(n^2+n+1/2)
=[(n-1)n+1/2][n(n+1)+1/2]
故原式=
(0*1+1/2)(1*2+1/2)(2*3+1/2)(3*4+1/2)...(18*19+1/2)(19*20+1/2)
---------------------------------------------------------------------
(1*2+1/2)(2*3+1/2)(3*4+1/2)(4*5+1/2)...(19*20+1/2)(20*21+1/2)
(0*1+1/2)
=----------
(20*21+1/2)
=1/841