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Today:
In particular, we focus on an infinite sum of increasing powers of $x$ -- a polynomial of "infinite degree", essentially.
Last time, at the buzzer, we discovered that the tremendously important exponential function \[ e^x=\sum_{k=0}^\infty\frac{x^k}{k!} \]
We'll see that most other functions we deal with can be expressed this way, and it's key for computing approximations to these functions (along with the tools we learned about infinite series -- because when you replace $x$ with a value, we just have an infinite series, which we can approximate if it's convergent).