Table of Newtonian series

Alright kiddo, a table of newtonian series is a way to calculate the value of a function using a special formula called the Newton series.

Sometimes, we have a complicated function that we want to know more about, but it's hard to work with directly because it has a lot of different parts. The Newton series helps us break that big function down into smaller parts that are easier to understand.

First, we choose a starting value (let's call it "a") that we can easily calculate the function for. Then, we find the first derivative of the function at that value of "a" (which is just a fancy way of saying we figure out how much the function changes when we move a tiny bit away from "a"). We plug those two things into the Newton series formula, and then repeat the whole process again using our new answer as our new starting value.

We keep doing this until we have a good enough answer or we've gone through a certain number of steps. It may sound complicated, but it's really just a way to break down a big problem into smaller pieces to make it easier to solve.