Question

taylor series question

Answer 1

\[\frac{ x }{ 1+x^{2} }\] x=0

Answer 2

just divide .... itll create the series

Answer 3

sorry

Answer 4

\[\frac{ x }{ (1+x)^{2} }\]

Answer 5

do I still just divide it?

Answer 6

ok, you may want to elaborate on what it is you are goig for.

and yes, expand th ebottom and do the division should work out just as well

Answer 7

we are just suppose to express it as a series at x=0 and I don't see the results of the division

Answer 8

the order of division might play into it, put the constant out front


x -2x^2+3x^3-4x^4 ... i think theres a pattern
---------------------
1 + 2x + x^2 | x
-(x + 2x^2 + x^3 )
-2x^2 -x^3
-(-2x^2 -4x^3-2x^4)
3x^3+2x^4
-(3x^3 + 6x^4+ 3x^5)
-4x^4 -3x^5

Answer 9

\[\sum_{n=0}^{\infty}(-1)^{n+1}nx^n\]

Answer 10

my exponent on -1 might be off i dont always get that right the first time :)

Answer 11

nah its good

Answer 12

is that a common method for finding the series. Would this work for 1/(1-x) because I originally though the way were suppose to solve it was relate it to that some way.

Answer 13

it works for the most part yes, i havent come across one where it hasnt

Answer 14

ok thank you for the trick

Answer 15

yep