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.