How can I rewrite this series of equations?

Question

I have the following series of equation:

$m_1=m_1$

$m_2=m_1q_1$

$m_3=m_1q_1q_2$

$m_4=m_1q_1q_2q_3$

and so on till some $i=M$.

What I want is to write this in one function such that by plugging in any $i$ it outputs me the corresponding right hand side of the function.

What I found is the following:

$m_i=m_1\prod_{2}^i (q_{i-1})$

However, this only holds for $i>1$.

It it possible to construct such a thing for all $i$>0?

Answer 1

The formula $$m_i = m_1 \prod_{j=1}^{i-1} q_j$$ holds for all $i>0$, under the convention that an empty product is $1$.