I’d like to reach out to the community to find an improved way of approaching a specific, common problem type (finding the Taylor coefficients in various binomial series expansions; both a) the general term and b) the first 4-5 nonzero terms).
I have been working on many of these problems recently, and my approach just feels inefficient. And although I have found questions on Math.SE about “solving more efficiently,”$^{\color{red}1}$ such questions clearly have a subjective element, and so seem in a bit of a grey area, in terms of being on-topic (although, when an answer is available, the Q&A together can provide a great practical resource, for many).
In addition to using this, personally, I would also want to share any great simplification with my students, so I wasn’t sure if this eventual end automatically framed it as a question for the Math Education SE, or if there is also room on Math.SE for asking about optimized methods / streamlining computations etc?
$^{\color{red}1}$: e.g. the answer to this question provides a really useful shortcut in the computation of finite binomial expansions.