Find the sequence [itex](B_nf)[/itex] of Bernstein's polynomials in(adsbygoogle = window.adsbygoogle || []).push({});

a) f(x)=x and

b) [itex]f(x)=x^2[/itex]

Answers (from my textbook):

a) [itex]B_nf(x) = x[/itex] for all n.

b) [itex]B_nf(x) = x^2 + \frac{1}{n} x (1-x)[/itex]

I know that the bernstein's polynomial is:

[itex]B_nf(x) = \sum_{k=0}^n f (\frac{k}{n}) \binom{n}{k} x^k (1-x)^{n-k} [/itex]

...but I don't know how they got the answer from this...

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# Homework Help: Bernstein's polynomial

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