let-S-n-p-k-0-n-k-p-prove-that-S-n-p-1-p-1-n-1-p-1-k-0-n-1-C-p-1-k-S-n-k-

Question Number 52669 by maxmathsup by imad last updated on 11/Jan/19

l e t S_{n} (p) = \sum_{k = 0}^{n} k^{p}

p r o v e t h a t S_{n} (p) = \frac{1}{p + 1} {{(n + 1)}^{p + 1} - \sum_{k = 0}^{n - 1} C_{p + 1}^{k} S_{n} (k)}