"Counting in their heads"  1895 oil painting

08092020, 02:24 PM
Post: #6




RE: "Counting in their heads"  1895 oil painting
An elegant way to get sum of squares formula is with geometry.
sumofnsquares = 1/3 * (2*n+1) * n*(n+1)/2 = n*(n+1)*(2*n+1)/6 Falling factorial derivation is also simple: s(x) = x² = x + x*(x1) = x^{1} + x^{2} S(x) = Σ(s(t), t=0 .. x1) = x^{2}/2 + x^{3}/3 = x*(x1)*(1/2 + (x2)/3) = x*(x1)*(2*x1)/6 // note: sumofnsquares = S(n+1) 10²+11²+12²+13²+14² = S(15)  S(10) = 15*14*(301)/6  10*9*(201)/6 = 35*(301)  15*(201) = (1050300)  (3515) = 730 

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