Thread: Sequences and series.

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:


-

- A sequence is then given such as

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:



-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.

Originally Posted by track02

-Lastly, I'm struggling in creating the MacLaurin Series for the function:

Write:



and use:



Regards.

Fernando Revilla

Thanks for the assistance.

Correct me if I am wrong, but by treating [LaTeX ERROR: Convert failed] as [LaTeX ERROR: Convert failed] you are allowing the use of sigma notation for an infinite geometric series?

Which will have the same effect as using a MacLaurin Series?

Also, does anyone have any idea where I can find some information regarding my first issue, I've been searching and still nothing!

Thanks again.

For large n we have



means that



that is that these functions have the same order of magnitude.

Originally Posted by track02

Correct me if I am wrong, but by treating [LaTeX ERROR: Convert failed] as [LaTeX ERROR: Convert failed] you are allowing the use of sigma notation for an infinite geometric series?

Right.

Which will have the same effect as using a MacLaurin Series?

Right, as a consequence of unicity of the Taylor expansion.

Regards.

Fernando Revilla