Question

小学四年级奥数1/1*2*3+1/2*3*4+.+1/20*21*22

Answer 1

1/n(n+1)(n+2)=(1/n(n+1)-1/(n+1)(n+2))/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

=(1/1*2-1/21*22)*1/2

=(1/2-1/462)/2

=115/462