Convergence of the recursive sequence $q_n = 1 - (1-pq_{n-1})^k$

Question

I have to proove that the sequence $$ q_n = 1 - (1-pq_{n-1})^k, q_0 = 1 $$ converges to a point in $[0,1]$ for $p, q_n \in [0,1]$ for all $n$ and $k \geq 1$.

The sequence $q_n$ is a probability measure so is obviously bounded below by $0$. But I have some difficulties prooving that the sequence is decreasing. Thanks in advance!