\begin{equation*} M(0) = 1 \end{equation*}

\begin{equation*} M'(0) = \frac{r}{p} \end{equation*}

\begin{equation*} M''(0) = \left ( \frac{r(1-p)}{p^2} \right )^2 + \left ( \frac{r}{p} \right )^2 \end{equation*}