Proof for \sum_{k=1}^n k^a equaling a sum of fractions

nrgiizr0ib6

nrgiizr0ib6

Answered question

2022-04-28

Proof for k=1nka equaling a sum of fractions

Answer & Explanation

zavesiljid

zavesiljid

Beginner2022-04-29Added 21 answers

Assuming that we know the expression of
k=1nk,k=1nk2,,k=1nkp1
then since by telescoping
k=1n(k+1)p+1kp+1=(n+1)p+11
and
(k+1)p+1kp+1=s=0p(p+1s)ks
hence we can find
k=1nkp=1p+1((n+1)p+1s=0p1(p+1s)k=1nks1)

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