Question

Determine if the following is a power series.

A) x-x^2+x^4-x^8+x^11-...


B) x^5+x+2


C) (8/x)+(8/x^2)+(8/x^3)+(8/x^4)+...

Answer 1

I'd guess that A is a power series. It seems like A follows the pattern of
\[\left\{ a_{n} \right\}= \sum_{i=1}^{n}-1*x^{k_{i}}_{i}\]
\[k_{n} = \sum_{i=1}^{n-1} k_{i} +1\]

In my mind, it stays true with the exception of k=1 and k=11. If you can figure out a way to account for those terms than you should have yourself a power series.

Answer 2

seem good so far?

Answer 3

i'm confuse

Answer 4

you are should be lol, I guess another way of saying what I wrote is that your series is a power rule because the powers increase in some form of sums with each other.

Answer 5

\[\[\sum_{x=0}^{\infty} C_nx^n\]

Answer 6

this is the power series about x=0 right?

Answer 7

pretty much. I'm not an expert, but it seems like the series does follow that pattern..unless the x^11 is a hint that this series is somewhat random

Answer 8

and your c should equal negative one

Answer 9

so c is a power series?

Answer 10

no...I meant the Csubn sigma thing in your comment. I have not given C a look yet

Answer 11

well, what exactly is a power series?

Answer 12

Are you sure that the last term in A) should be 11 and not 10?