"Counting in their heads"  1895 oil painting

08082020, 07:42 PM
Post: #3




RE: "Counting in their heads"  1895 oil painting
(08082020 05:29 PM)EdS2 Wrote: calculate (10²+11²+12²+13²+14²)/365 With only 5 terms, it is trivial to calculate. (xy)² + (x+y)² = 2(x²+y²) 12² + (11²+13²) + (10²+14²) = 5*12² + 2*(1+4) = 730 730/365 = 2  Here is a way to fit it to polynomial, then "integrate" (see Funny Factorial and Slick Sums) We know f(x) is quadratic, thus only 3 points needed. Code: x f(x) Δ Δ² \(f(x) = 100 + 21\binom{x}{1} + 2\binom{x}{2}\) \(F(x) = \sum_{t=0}^{x1} f(t) = 100\binom{x}{1} + 21\binom{x}{2} + 2\binom{x}{3}\) F(5)/365 = (100*5 + 21*10 + 2*10) / 365 = 730/365 = 2 

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