prove that $\Sigma_{-\infty}^{\infty}a_iB_i^k(x)=x $

Question

It's a question in chapter 6 of "Numerical Analysis" by kincaid:

prove that if $a_i=k^{-1}(t_{i+1},t_{i+2} \dots,t_{i+k})$, then $$\Sigma_{-\infty}^{\infty}a_iB_i^k(x)=x \ \ \ \ (k\geq1)$$ where $B$ is stand for B-spline.

any help would be appreciated