Use the power series 1/1+x = ∑[infinity]ₙ ₌ ₀(-1)ⁿxⁿ to determine a power series, centered at, for the function.

f(x) arctan 3x
f(x) ∑[infinity]ₙ ₌ ₀

Identify the interval of convergence. (Enter your answer using interval notation.)