# How to solve?

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

Help would be greatly appreciated.

Victor

Note by Victor Loh
4 years, 9 months ago

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

- 4 years, 9 months ago