Write the following as an infinite goemetric series...?

Question

Write the following as an infinite geometric series, note any restrictions on "r".


f(x)=1/(1-x)

and

f(x)=1/(1-9x^2)

Answer 1

1/(1-x) = 1 + x + x^2 + x^3 + x^4 + ...

1/(1-9x^2) = 1 + 9 x^2 + 81 x^4 + 729 x^6 + ... + 9^(n-1) x^2(n-1) + ...

Answer 2

scythian1950 has got it right, I would just add that the series expansions hold for |x|<1 in the first case and |x|<1/3 in the second.