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=5an−1a_n = 5a_{n-1}an=5an−1 with a0=1a_0 = 1a0=1?
A(x)=11−5xA(x) = \frac{1}{1-5x}A(x)=1−5x1
A(x)=11+5xA(x) = \frac{1}{1+5x}A(x)=1+5x1
A(x)=x1−5xA(x) = \frac{x}{1-5x}A(x)=1−5xx
A(x)=51−xA(x) = \frac{5}{1-x}A(x)=1−x5