Looking for Calculus Geniuses Power Series
So I have this test tomorrow on Power Series. I understand how to find a taylor polynomial, error estimation, interval of convergence, and all that good stuff.
But I have serious trouble with finding the function when given the sigma/summation notation.
[url=http://i.imgur.com/Q0TF3qz.png]Here's two examples.[/url]
I've memorized the series for 1/(1-x), sinx, cosx, and e^x. Those are the ones my teach always base the problems off of.
Does anyone have a process that they could share with me?
May 14, 2015
3 Comments • Newest first
For 3, note that [url=http://i.imgur.com/Uau3UJd.jpg]log(1-x) looks like this[/url]
For 8, note that [url=http://i.imgur.com/dLWx6Dh.jpg]cosh(x) looks like this[/url]
Write out the terms for both series, and apply transformations to both side until the infinite series becomes the one in the question. The log(1-x) series should be something you should know off the bat (or at least know how to derive it). The cosh(x) series might not seem obvious at first glance but can be derived from its exponential representation.
Sequences and series were the only part of Calc II I did well on.
You just gotta memorize the basic ones (which you already did) and just play around with the sums given and attempt to break them down into the basic functions. That's all you can do.
I would recommend using the Ratio Test for the first problem and possibly the second one. I'm too lazy to try it out right now considering I just took my final on that last Tuesday LOL and just need a break from it all. I hope it helps at all