Let $R$ a ring, and let $\displaystyle R[[x]]=\left\{\sum_{k=0}^{\infty}a_k x^k\;\middle\vert\; a_k\in R\right\}$ with addition and multiplication as defined for polynomials. We have that $R[[x]]$ is a ring containing $R[x]$ as a subring.
How to prove that if $a_0\in R$ is a unit, then $\displaystyle\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$?