I am stuck on a question regarding discrete random variable. The question is as follows:

The probability mass function of $X$ with $x \in \mathbb{N}:=\{0,1,2, \ldots\}$ satisfies the following:

\begin{align}
\frac{(=)}{(=+1)}=x+1
\end{align}

I am asked to find $(=0)$ and identify the distribution of $X$

I worked out that $(=0)=(=1)$ from the given PMF but not sure what to do next and how to identify the type of distribution of $X$.

Any help is greatly appreciated.