I finally figured out how to approach the Taylor series question Katie asked this morning! The good news is: as I said this morning, once we had the key, it would be easy to unlock the rest of the problem. The bad news is: “easy” is a relative term; this still ended up being long. (Tip: this is probably too long a question to give on a test.) The other good news is that even though there are many steps, none of them require a huge leap.

The link to the notes is here and the document is also in the Dropbox folder containing COLD session notes. Apologies, but it’s unlikely I’ll be able to record a video of this one this week (maybe ever), so the notes will have to do for now. Please let me know if you have any questions about it.

Hopefully the color coding makes sense. I was going to skip finding the interval of convergence, but it was actually not too bad to track how the I of C changes as we manipulate the functions, so I snuck it in afterward in the appropriate places in brown.

You’ll notice that I split this into two warmup exercises before getting to the actual question that was asked. If you just want to see how the warmup exercises were used to find the series, skip to the last page.

Good luck!