Solution
= Solution
Apply the <Leibniz rule for divided differences> to $(x-t)_+^{k-1}=(x-t)(x-t)_+^{k-2}$. Only the zeroth and first divided differences of the linear factor survive. After applying the normalization, this gives the <Cox-de Boor recursion formula>
$$
\boxed{N_{i,k}(t)=\frac{t-t_i}{t_{i+k-1}-t_i}N_{i,k-1}(t)
+\frac{t_{i+k}-t}{t_{i+k}-t_{i+1}}N_{i+1,k-1}(t)}.
$$