1. **State the problem:** Find the interval of convergence of the series $$1 + \frac{2}{3}x + \frac{4}{9}x^2 + \cdots$$ 2. **Identify the general term:** The series can be written as $$\sum_{n=0}^\infty a_n x^n$$ where $$a_n = \frac{2^n}{3^n} = \left(\frac{2}{3}\right)^n$$. 3. **Use the ratio test for convergence:** The ratio test states that the series converges if $$\lim_{n \to \infty} \left| \frac{a_{n+1} x^{n+1}}{a_n x^n} \right| < 1$$. 4. **Calculate the limit:** $$\lim_{n \to \infty} \left| \frac{\left(\frac{2}{3}\right)^{n+1} x^{n+1}}{\left(\frac{2}{3}\right)^n x^n} \right| = \lim_{n \to \infty} \left| \frac{2}{3} x \right| = \left| \frac{2}{3} x \right|$$. 5. **Set the inequality for convergence:** $$\left| \frac{2}{3} x \right| < 1 \implies |x| < \frac{3}{2}$$. 6. **Conclusion:** The interval of convergence is $$-\frac{3}{2} < x < \frac{3}{2}$$. **Answer:** (a) $$-\frac{3}{2} < x < \frac{3}{2}$$