Question

f(x)=x/(9+x^2), find power series. Any hints?

Answer 1

First find the power series (assuming it is centered at 0) of 1/(9+x^2). Then multiply each term by x.

Answer 2

yes a swell idea.

Answer 3

1/(1+x), now should i sub x=(x/3)^2,? i mean is it legal

Answer 4

and for
\[\frac{1}{9+x^2}\] start with
\[\frac{\frac{1}{9}}{1+\frac{x^2}{9}}\]

Answer 5

@iHelp Yes, that's legal. :D

Answer 6

sort of legal. idea is to make it look like
\[\frac{1}{1+x}\]if you can

Answer 7

that'll do it

Answer 8

series n=1 to infin of (-1)^n((x/3)^2n)(x/9)? someone check for me plz ?

Answer 9

yes i think so but you can clean it up because you have x twice

Answer 10

you know you have
\[\frac{1}{9}\sum(-1)^n(\frac{x}{3})^{2n} x\]

Answer 11

so the other x should be included in the first one

Answer 12

i c, thanks.

Answer 13

\[\frac{1}{9}\sum(-1)^n\frac{x^{2n+1}}{3^{2n}}\] might look better although of course it is the same