If is a polynomial of degree such that , , ,

MATHEMATICS · Multi correct · A Level · Mathematics · Proof · Proof

Problem

If f(x)f(x) is a polynomial of degree nn such that f(0)=0f(0)=0, f(1)=12f(1)=\frac{1}{2}, …\ldots, f(n)=nn+1f(n)=\frac{n}{n+1}, then the value of f(n+1)f(n+1) is (1) 11, when nn is even (2) nn+2\frac{n}{n+2}, when nn is odd (3) 11, when nn is odd (4) nn+2\frac{n}{n+2}, when nn is even

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