Probability of events for beta-geometric distribution

If we have a beta-geometric distribution X with pdf $P(X=k\mid \alpha ,\beta )=\frac{Beta(\alpha +1,k+\beta )}{Beta(\alpha ,\beta )}$.

If we have a beta-geometric distribution X with pdf $P(X=k\mid \alpha ,\beta )=\frac{Beta(\alpha +1,k+\beta )}{Beta(\alpha ,\beta )}$.