1乘2乘3+2乘3乘4+3乘4乘5 +.+N乘(N+1)乘(N+2)=
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1×2×3+2×3×4+3×4×5+.+n(n+1)(n+2) =1/4【1×2×3×4-0×1×2×3】+1/4【2×3×4×5-1×2×3×4】+1/4【3×4×5×6-2×3×4×5】+.+ 1/4【n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)】 =1/4n(n+1)(n+2)(n+3)

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