Find the interval of convergence?

Question

Find the interval of convergence for ∑ (x^n)/(2^n) from n=0 to infinity.

The answer is (-2, 2). Please show all your work. Thank you.

Answer 1

(x/2)^n

converges if the ratio is between -1 and 1:

-1 < x/2 < 1

-2 < x < 2