Suppose that, \(\displaystyle \forall k \in \mathbb{N}\) : \(\displaystyle a_k\leq|p(b_k)|\), when \(\displaystyle p\) is polynomial so that \(\displaystyle p(0)=0\).

Prove that if \(\displaystyle \sum_{k=1}^{\infty} b_k \) converges so then \(\displaystyle \sum_{k=1}^{\infty} a_k \) converges also.