Hey there.
I'm wondering if anyone here will be able to assist with the following issues:
1. I'm currently working on questions asking me to:
- $\displaystyle Find \: \alpha \: so \: that \: a_n \: = \: O(n^\alpha)$
- A sequence is then given such as $\displaystyle n^2 \: + \: n \: + \:1 $
I'm curious as to what type of questions these are, they are listed under "Order of magnitude" in my notes but searching for this returns no useful resources.
2. MacLaurin Series
-Lastly, I'm struggling in creating the MacLaurin Series for the function:
$\displaystyle \frac{1}{x^2 + 1} $
-I have tried differentiating but this becomes quite difficult after the third derivative or so. I am guessing there is another method to solve this?
Any help concerning either of these issues would be greatly appreciated.
Thank you.