What is the pros and cons of symbolic and numerical approach?

I always feel symbolic approach is much convenient in terms of plotting. However, I want to know what is pros and cons of both approaches?

Answer 1

[Matt J]

I would expect numerical computation to be faster.

[Walter Roberson]

Shall we race the calculation of an infinite sum? :)

Answer 2

[Walter Roberson]

There are some calculations which have no known or no possible closed analytic form. Those calculations must be done numerically.

There are some (but far from "all") calculations that are faster numerically.

Symbolic has the advantage for every other situation I can think of at the moment. I might think of something different when I wake up further.