I’m writing this blog post because when I first came across Taylor series I found that a lot of my previous intuitions for mathematics were suddenly inadequate. It took time for me to build intuition not only for how these things work but why they are important. I hope this post will be illuminating for those just beginning to learn about Taylor series and also those who have some experience with them but haven’t quite wrapped their heads around them yet.
First, recall that a series is defined as a finite or infinite sum of terms. For example:
The above is a finite series. We can sum series to finite amounts or to infinite amounts:
And, we say that these infinite series either converge to a specific finite number, or as in the case above, diverge towards infinity. Series don’t just represent numerical quantities, though. We can use them to conveniently represent certain kinds of polynomials. For example:
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Check out some of our previous blog posts related to mathematics below!