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. $$S=\left\{"p","e","r","s","o","n"\right\}$$ What is $\frac{1}{6}{\sum }_{s\in S}s$? A mean person…