Finding sum of a finite series. Consider the series 
$$\frac {q_1} {p_1} + \frac {q_1 q_2} {p_1 p_2} + \cdots + \frac  {q_1q_2 \cdots q_n} {p_1 p_2 \cdots p_n}$$ where $p_i + q_i = 1$ and $0 < p_i < 1$ and $0 <  q_i < 1$  for all $i=1,2, \cdots , n$.
How can I find the sum of this series? Please help me in this regard.
Thank you very much.

let
$$
\frac {q_1} {p_1} + \frac {q_1 q_2} {p_1 p_2} + \cdots + \frac  {q_1q_2 \cdots q_n} {p_1 p_2 \cdots p_n}=\frac{a_n}{p_1p_2\cdots p_n}
$$
$\implies a_1=q_1$ and $a_np_{n+1}+q_1q_2\cdots q_{n+1}=a_{n+1}$.
