A riddle, guess the word from the sum

What is [ \left(a\sum_{n=2}^\infty w^n\right)! ]

If you can't figure it out, here are 2 hints.

Hint 1: What is \sum_{V\subseteq U} \dim(V)? Where U is a vector space of dishes for a yum cha.

Hint 2: On the internet, you will see the following variation. [ \left(a\sum_{n=2}^\infty w^n\right)!!!! ]

Answer: "awesome!" and the answer for the hint is "dim sum"

Here is an extra riddle for fun. [ S = \set{"p","e","r","s","o","n"} ] What is \frac{1}{6} \sum_{s\in S} s? A mean person...