Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.)

Question

Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.)

f(x)= x/(1-x^3)

sum from n=0 to infinity [?] provided |x| < [?]

Answer 1

I think you will get your answer by long division.

1/(1-x³) = 1 + x³ + x⁹ + ...

and the interval of convergence is |x|<1