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Sequences, series, and function approximation
Sequences, series and approximating functions. Maclaurin and Taylor series.
All content in “Sequences, series, and function approximation”

Sequence convergence and divergence

Now that we understand what a sequence is, we're going to think about what happens to the terms of a sequence at infinity (do they approach 0, a finite value, or +- infinity?).

Tests for convergence and divergence

We will now deepen our convergence and divergence tool kits by exploring a series of "tests" we can apply to determine the behavior of some series.

Power series function representation using algebra

Now that we're familiar with the idea of an infinite series, we can now think about functions that are defined using infinite series. In particular, we'll begin to look at the power series representation of a function (and the special case of a geometric series). In later tutorials, we'll use calculus to find the power series of more types of functions.

Maclaurin series and Euler's identity

In this tutorial, we will learn to approximate differentiable functions with polynomials. Beyond just being super cool, this can be useful for approximating functions so that they are easier to calculate, differentiate or integrate. So whether you will have to write simulations or become a bond trader (bond traders use polynomial approximation to estimate changes in bond prices given interest rate changes and vice versa), this tutorial could be fun. If that isn't motivation enough, we also come up with one of the most epic and powerful conclusions in all of mathematics in this tutorial: Euler's identity.