高中數學討論區

尋找規律

Σ k=1到n k^p=?
p=1時,原式=(1/2)n+(1/2)n^2
p=2時,原式=(1/6)n+(1/2)n^2+(1/3)n^3
p=3時,原式=(0/1)n+(1/4)n^2+(1/2)n^3+(1/4)n^4
p=4時,原式=(-1/30)n+(0/1)n^2+(1/3)n^3+(1/2)n^4+(1/5)n^5
p=5時,原式=(0/1)n+(-1/12)n^2+(0/1)n^3+(5/12)n^4+(1/2)n^5+(1/6)n^6
p=6時,原式=(1/42)n+(0/1)n^2+(-1/6)n^3+(0/1)n^4+(1/2)n^5+(1/2)n^6+(1/7)n^7
............
找不到Σ k=1到n k^p=?的規律==||

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