\displaystyle
X\sim G(p)\\
\sum_{n\in\mathbb{N}} P(X^2>n)=1 \overset{Zad. 4.20}{\iff} \mathbb{E}[X^2]=1\\
\mathbb{E}X=\frac{1}{p}\\
Var\ X=\mathbb{E}[X^2]-(\mathbb{E}X)^2=\frac{1-p}{p^2}\\
\dots\\
\mathbb{E}[X^2]=\frac{2-p}{p^2}=1\\
p_{1,2}=\dots