Find a generating function $a_n$, the number of partitions that add up to at most $n$.
So I know that if it were asking the number of partitions of the integer $n$, I would have my generating function as
$$ g(x) = \frac{1}{(1-x)(1-x^2)(1-x^3)\cdots} $$
But for now, all I can come up with to handle the "at most" condition is $$ \prod_{r=1}^{m\leq n} \frac{1}{1-x^r}, \text{ for some } m. $$ And I really don't think that this is correct. (No solution provided).