Answer Happy

T/F?
1. Every power series n=0∑​an​xn converges at x=0. 2. The power series n=0∑∞​an​(x−a)n converges on an interval centered at x=a. 3. The power series n=0∑∞​xn converges if ∣x∣<1. 4. 1−x1​=n=0∑∞​xn for all x with ∣x∣<1