Consider the lacunary power series f(x)=∑n=0∞x2n=x+x2+x4+x8+x16+⋯f(x) = \sum_{n=0}^{\infty} x^{2^n} = x + x^2 + x^4 + x^8 + x^{16} + \cdotsf(x)=∑n=0∞x2n=x+x2+x4+x8+x16+⋯. What is the radius of convergence?
R=0R = 0R=0 (radius zero)
R=1R = 1R=1
R=∞R = \inftyR=∞ (entire function)
R=eR = eR=e