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$P(x)$ is a polynomial of degree $n$ that satisfies $P(k)=\frac{k}{k+1}$ for $k=0,1,2,3,...,n$. Find $P(n+1)$.

What have I tried: I have literally no idea how to do questions of this kind. Also, in general what is the method solving such questions where they say a polynomial behaves a certain way with a range of numbers and expect you to extrapolate the next value?

Thank you!

WilliamKin
  • 585
  • The general method that always works is Lagrange interpolation. In practice, whenever you have a formula for $P(k)$ rather than just arbitrary data, the quickest approach is generally "find a closely related polynomial whose roots you know," as in the accepted answer to the linked problem. – Micah Jun 23 '15 at 13:12
  • Ok I see thank you!! @Micah – WilliamKin Jun 23 '15 at 16:38

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