grandes-ecoles 2021 Q35

grandes-ecoles · France · centrale-maths2__pc Sequences and Series Evaluation of a Finite or Infinite Sum
The polynomials $B_m$ are defined by $$\forall m \in \mathbb{N}, \quad B_m(x) = \sum_{k=0}^m \binom{m}{k} b_k x^{m-k}.$$
Determine $B_0, B_1, B_2$ and $B_3$.
The polynomials $B_m$ are defined by
$$\forall m \in \mathbb{N}, \quad B_m(x) = \sum_{k=0}^m \binom{m}{k} b_k x^{m-k}.$$

Determine $B_0, B_1, B_2$ and $B_3$.