1. If $p(x)$ is an $n$-degree polynomial, and satisfies $p(k)=\frac{k}{k+1}(k=0,1, \cdots, n)$, find $p(n+1)$.
1. When $n$ is even, $p(n+1)=\frac{n}{n+2}$; when $n$ is odd, $p(n+1)=1$. Hint: Construct the auxiliary polynomial $f(x)=$ $(x+1) p(x)-x$.

