数列求和 1×2+2×3+3×4+……+(n-1)(n-2)

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数列求和1×2+2×3+3×4+……+(n-1)(n-2)数列求和1×2+2×3+3×4+……+(n-1)(n-2)数列求和1×2+2×3+3×4+……+(n-1)(n-2)n(n-1)=(1/3)(

数列求和 1×2+2×3+3×4+……+(n-1)(n-2)
数列求和 1×2+2×3+3×4+……+(n-1)(n-2)

数列求和 1×2+2×3+3×4+……+(n-1)(n-2)
n(n-1)=(1/3)((n+1)n(n-1)-n(n-1)(n-2))
然后 1×2+2×3+3×4+……+(n-1)(n-2)
=0×1+1×2+2×3+3×4+…+(n-1)×n
=(1/3)(2×1×0-1×0×(-1))+(1/3)(3×2×1-2×1×0)+...+(1/3)((n+1)n(n-1)-n(n-1)(n-2))
(裂项相消)
=(1/3)((n+1)n(n-1)-1×0×(-1))
=1/3n(n+1)(n-1)