用数学归纳法证明:1×2×3+2×3×4+…+n×(n+1)×(n+2)=n(n+1)(n+2)(n+3)4(n∈N*).

问题描述:

用数学归纳法证明:1×2×3+2×3×4+…+n×(n+1)×(n+2)=

n(n+1)(n+2)(n+3)
4
(n∈N*).

证明:(1)当n=1时,左边=1×2×3=6,右边=1×2×3×44=6=左边,∴等式成立.(2)设当n=k(k∈N*)时,等式成立,即1×2×3+2×3×4+…+k×(k+1)×(k+2)=k(k+1)(k+2)(k+3)4.  则当n=k+1时,左边=1×2...