Next Step Polynomial

Algebra Level 3

If f(x)f(x) is a polynomial of odd degree nn such that f(0)=0,f(1)=12,,f(n)=nn+1f(0)=0,f(1)=\dfrac{1}{2},\ldots,f(n)=\dfrac{n}{n+1}, then find f(n+1).f(n+1).

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