1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+.+1/48×49×50
=(1/2)*(1/1×2-1/2×3)+(1/2)*(1/2×3-1/3×4)+.(1/2)*(1/48×49-1/49×50)
=(1/2)*(1/1×2-1/2×3+1/2×3-1/3×4+1/3×4.+1/48×49-1/49×50)
=(1/2)*(1/1×2-1/49×50)
=(1/2)*(1224/2450)
=612/2450
=306/1225