P\left( {X_n = k} \right) = \frac{{qp^k \left( {1 - p} \right)^{n - k} }}
{{1 - \left( {1 - q} \right)\left( {1 - p} \right)^n }} + \frac{{\left( {1 - q} \right)}}
{{1 - \left( {1 - q} \right)\left( {1 - p} \right)^n }}\sum\limits_{i = 1}^k {\left( \begin{gathered}
 k \hfill \\
 i \hfill \\ 
\end{gathered} \right)p^i \left( {1 - p} \right)^{n - i} P\left( {X_{n - i} = k - i} \right)}