Editing 2605: Taylor Series

In mathematics, the {{w|Taylor series}} of a function is an infinite sum of terms that is expressed as the function's {{w|Derivative|derivatives}}. Their expressions, usually referred to as "expansions," continue without end. Taylor series are useful for deriving numerical and {{w|Symbolic integration|symbolic}} forms of {{w|Irrational number|irrational}} values, {{w|Machin-like formula|such as π}}, to make them easier to integrate or otherwise manipulate with calculus.[https://www.mathsisfun.com/algebra/taylor-series.html] However, because they involve difficult calculus operations, and can be annoyingly tedious to {{w|Numerical analysis|calculate by hand}}, they are often not loved by math students{{citation needed}}.

[[Miss Lenhart]] appears to be teaching a class about how to use a Taylor series. She has explained what one is, and how it is used. She presumes her students want to keep learning about the series, in that they, "wish it would never end." She then says "Good news!" because the Taylor series does not end, each term being smaller than the last. The cartoon's humor is based on contrasting the idea of wishing the series will never end, which is ordinarily expressed regarding long-running sequences of enjoyable events, with the infinite nature of the Taylor series, which is probably not appreciated by her students struggling to understand why the sums {{w|Convergent series|converge}} to their resulting value.

The title text is a reference to the common practice among physicists and engineers of abbreviating the Taylor series to only the first few terms, typically one or two, in order to simplify the mathematics of their models. The title text is also a pun on the use of the word "series" to refer to a television program. It symbolizes the terms of the mathematical series as a {{w|metaphor}} with a television season, suggesting that only the first term is useful. It makes fun of the common sentiment against bad {{w|screenwriting}} of a series by saying that, "The series should have been cancelled after the first season," replacing "season" with "term." It should be noted that there do indeed exist functions for which the Taylor series has effectively only one term -- specifically, functions with a degree of zero, or where y is a constant value. All of the derivatives of these functions are zero, and thus the Taylor series is effectively a single term -- just the value itself.