What is the generating function A(x)=∑n=0∞anxnA(x) = \sum_{n=0}^{\infty} a_n x^nA(x)=∑n=0∞anxn for the sequence an=3an−1a_n = 3a_{n-1}an=3an−1 with a0=1a_0 = 1a0=1?
11−3x\frac{1}{1-3x}1−3x1
11+3x\frac{1}{1+3x}1+3x1
31−x\frac{3}{1-x}1−x3
1−3x1-3x1−3x