Question

Power Series:

Answer 1

so normally a power series is represented by an x^n or an(x-c)^n now I've seen some questions ask about a taylor power series or geometric series, so what exactly does power series do? It can be applied to other series as well?

Answer 2

A power series is a specific type of infinite sum that includes the variable x and is based upon n. So it's essentially a function of x with an infinite number of terms increasing by x.

\[\sum_{}^{} a _{n}x^n\]

Answer 3

mhm

Answer 4

I mean, I suppose that doesn't explain it well enough, but I'm not sure what you know. What can I elaborate on?

Answer 5

Taylor and Mclaurin Power series are approximating functions such as e^x, sinx with polynomials by making infinite polynomials that have the same first, second, nth... derivative.

Answer 6

I'm just curious what changes when we do other types of powr seires... One says find the geometric power series for 1/(7-x) centered at 0

Answer 7

now or for a geometric series we would want to change it's form, but is that what we should be doing here?

Answer 8

1/(7(1-(x/7)))

Answer 9

Hmm this might help: http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeriesandFunctions.aspx
It's been a while and I don't really remember this all that much. I know there's a way to convert with the form 1/(1-x) to a power series. I could tell you a little about Mclaurin series, which is estimating a function centered at 0, but that's about it.

Answer 10

thanks

Answer 11

well I'm asked for a geo series, and another question is a taylor series...