1/n(n+1)(n+2)=[1/n(n+1)-1/(n+1)(n+2)]*1/2
1/(1×2×3)+ 1/(2×3×4)+1/(3×4×5)+……+ 1/(20×21×22)
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/20*21-1/21*22)*1/2
=(1/2-1/21*22)*1/2
=115/462
1/n(n+1)(n+2)=[1/n(n+1)-1/(n+1)(n+2)]*1/2
1/(1×2×3)+ 1/(2×3×4)+1/(3×4×5)+……+ 1/(20×21×22)
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/20*21-1/21*22)*1/2
=(1/2-1/21*22)*1/2
=115/462