How to solve?

Let f(x)f(x) be a polynomial of degree nn such that f(k)=kk+1f(k)=\frac{k}{k+1} for k=0,1,2,...,nk=0,1,2,...,n. Find f(n+1)f(n+1).

Help would be greatly appreciated.

Victor

Note by Victor Loh
5 years, 6 months ago

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Let g(x)g(x) be the polynomial g(x)=(x+1)f(x)x.g(x) = (x + 1) f(x) - x. What can you say about g(x)g(x)? (Think roots and degree.)

Jon Haussmann - 5 years, 6 months ago

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