Question

find the geometric power series for the function \[\frac{ 1 }{ 2+x }\] centered at 0

Answer 1

as you may recall:

\[\sum_{0}^{\infty} x^{n} = \frac{ 1 }{ 1 - x }\]

we want to put the function of x in the form of the formula so we can simply plug it in the series.

Answer 2

let me know if i should do the next step

Answer 3

im thinking the answer is \[\sum_{n=0}^{\infty} \frac{ -x ^{n} }{ 2^{n+1} }\] ?

Answer 4

it is. way to simplify. lol

Answer 5

oh, thank you!