Question

Find a power series representation for the function.
f(x) = 1/(9 + x)

sum n=0 to infinity ____________________?

Answer 1

rewrite it as
\[\frac{1}{9}\left(\frac{1}{1+\frac{x}{9}}\right)\]

Answer 2

then use
\[\frac{1}{1-x}=\sum_{n=0}^{\infty}x^n\] replacing \(x\) by \(-\frac{x}{9}\)

Answer 3

wrong:S