Show, that $ \displaystyle \sum_{k=0}^n \lambda_k(0)x_k^j = \begin{cases} 1 \ (j=0)\\0 \ (j=1,2,\ldots n)\end{cases}$, where $\lambda_{k}$ is the 'helper' polynomial from Langrange Interpolation polynomial, with given $n+1$ points $x_{0},...,x_{n}$ etc.
So basically it's easily provable, that
$\sum_{i=0}^{n}\left(x_{i}^{n}\lambda_{k}(x)\right)=x^n$. So what we've got here is $\sum_{k=0}^n \lambda_k(0)x_k^j=0^{j}$
So for $1\leq j$ it's clear that it's $1$, but what about $j=0$? $0^{0}$ is undefined, and I don't know what to do...