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 defined by an=3an−1a_n = 3a_{n-1}an=3an−1 with a0=1a_0 = 1a0=1?
A(x)=11−3xA(x) = \frac{1}{1-3x}A(x)=1−3x1
A(x)=11+3xA(x) = \frac{1}{1+3x}A(x)=1+3x1
A(x)=x1−3xA(x) = \frac{x}{1-3x}A(x)=1−3xx
A(x)=1−3xA(x) = 1-3xA(x)=1−3x