\begin{array}{l}
 \sum\limits_{n = 1}^{ + \infty } {P\left( {X^2 > n} \right)} = \sum\limits_{n = 1}^{ + \infty } {\sum\limits_{k = n + 1}^{ + \infty } {P\left( {X^2 = k} \right)} } = \sum\limits_{n = 2}^\infty {\left( {n^2 - 1} \right) \cdot P\left( {X = n} \right)} = \\ 
 = \sum\limits_{n = 2}^\infty {\left( {n^2 - 1} \right) \cdot q^{n - 1} p} = p\sum\limits_{n = 1}^\infty {n\left( {n + 2} \right)q^n } = \\ 
 \end{array}