In the follwoing problem, why does the solution with lagrange interpolation work only when i take number of given dataset ( x, f(x) pairs ) >= k+2
problem link
solution 1 - with k+2 points, [0 , k+1]
solution 2 - with k+1 points, [0,k]
@aryanc403 @l_returns @vijju123
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Because
sigma n = n*(n+1)/2 is degree 2 polynomial
sigma n^2 = n*(n+1)*(2n+1)/6 is degree 3 polynomial
…
sigma n^k is degree k+1 polynomial.
And in lagrange we need k+1 data points for a degree k polynomial for getting correct result.
Hence we need k+2 data points because it will be a k+1 degree polynomial
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