Question

sum of (3+9^n)/(9^n) as n approaches inf

Answer 1

seems unlikely that this converges since the terms do not go to zero

Answer 2

\[an=\lim_{n \rightarrow \infty }\frac{ 3+9^n }{ 9^n }=\lim_{n \rightarrow \infty }\left( \frac{ 3 }{ 9^{n} }+1 \right)=0+1=1\neq 0\]
Hence it diverges.