"Counting in their heads"  1895 oil painting

08122020, 01:32 AM
(This post was last modified: 08122020 01:37 AM by Albert Chan.)
Post: #20




RE: "Counting in their heads"  1895 oil painting
I was wrong. There seems to be a pattern to sum of powers formula after all ...
\( S_p = n c^p + \large {n^3n \over 12} \left( \binom{p}{2} c^{p2} + {3n^27 \over 20} \binom{p}{4} c^{p4} + {3n^418n^2+31 \over 112} \binom{p}{6} c^{p6} + {5n^655n^4+239n^2381 \over 960} \binom{p}{8} c^{p8} + \cdots \right) \) Example: 50^5 + 51^5 + 52^5 + ... + 150^5 // p=5, c=100, n=101 = 101*100^5 + 102*101*100/12 * (10*100^3 + (3*101^27)/20*5*100) = 1934166665000 

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