"Counting in their heads"  1895 oil painting

08112020, 12:43 PM
(This post was last modified: 08112020 12:45 PM by Gerson W. Barbosa.)
Post: #16




RE: "Counting in their heads"  1895 oil painting
(08112020 10:39 AM)Albert Chan Wrote: → sumofncubes = cn*(c² + (n²1)/4) That’s equivalent to what I’ve come up with, except that I have introduced a factor to generalize for evenly spaced sequences: sumofncubes = nc(c² + d²(n²  1)/4) where n = number of elements in the evenly spaced sequence c = central element d = interval distance For example, S = 33³ + 40³ + 47³ + 54³ + 61³ + 68³ n = 6 c = (33 + 68)/2 = 50.5 d = (68  33)/(n  1) = 7 S = 6×50.5(50.5² + 7²(6²  1)/4) = 902637 Likewise, sumofnsquares = n(c² + d²(n²  1)/12) Considering the similarities between both formulae, perhaps they somehow can be generalized for all positive integer powers. 

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