I only did several parts to show the way of thinking that should be used. I only did #9 because you can easily verify the answers in the back of the book.
(There might be unnecessary parenthesis in several spots because I write with pen and I didn’t want to start over and over again ._.)
Here’s the link. If there is anything wrong please comment :]
http://rpubs.com/thebunnyknight/179355
***Everything in the CURLY BRACES { } should be added continually to infinity. I forgot to show that in the starting problems, but I showed it in the last problem that has SQUARE BRACKETS [ ] instead.
Professor,
Is the format of the way I did (e) okay? The others are slightly flawed because of the curly braces infinite thing that I mentioned above. Is there a “cleaner” way of writing all of this out that you would prefer?
-Eric Lewis
Hi Eric. I haven’t checked *all* your arithmetic, but I’ll assume it’s correct! I can follow your work easily, so it’s fine to write it like this. Notice that when you’re finding specific coefficients, you have a choice. You can write out as many terms of each power series as you’ll need and then find the coefficient explicitly, or you can find a formula for *all* the coefficients at once, and then substitute the appropriate index to find the coefficient you’re asked for. It looks like you’ve secretly answered these the second way, since you have some … before the term you’re interested in as well as after. Either way is fine with me as long as I can follow it.
What is the other way to solve this?