Can someone hint me on solving the following equation to find $P^*$
\begin{equation} P^* =\sum^\infty_{n=m}\{P(m).P(R_{n\mid m} \} \end{equation}
Where, \begin{equation} P(m) = e^{-\lambda t}(\lambda t)^m / m! \end{equation}
\begin{equation} P(R_{n\mid m}) = \sum^{n}_{j=0}(-1)^jC^j_n(1 - j.\phi)^m \end{equation}
The final solution is as follows:
\begin{equation} P^* = (1 - e^{-\phi\lambda t})^n \end{equation}
NOTE: It is not a part of any exam or assignment, I am reading a resarch paper. and I have never solved equations where I have Summation of such peculiar terms...If someone doesnot want to give the whole solution,any hint would still be highly appreciated.