Analytic Combinatorics to asymptotically estimate the number of objects of size at most n? I have read some bits of Flajolet's and Sedgewick's book on Analytic Combinatorics.
I am quiet curious as how to asymptotically estimate the number of objects of size at most n.
Suppose for example that I specified a combinatorial class $A$. I also computed its generating function $A(z)=\sum\limits_n a_n z^n$. Therefore, studying the singularities of $A(z)$ yields an asymptotic estimate of the coefficient $a_n$, that represents the number of objects of size n.
How can I asymptotically estimate the number of objects of size at most $n$ ($\sum\limits_{k=0}^{n} a_n$)?
Ideally, I would seek a combinatorial interpretation that would let me re-use the generating function $A(z)$, but I am drying up!
Any thoughts?

Indeed, it does the trick!
B(z) = $A(z) \times \sum\limits_n z^n = \sum\limits_{n} \sum\limits_{k = 0}^n a_k z^n$
