$4$ pts

Use the Limit Comparison Test to determine the convergence or divergence of the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5^n+1}{8^n+1}.$ What is $b_n?$ What is the limit value $?$

The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5^n+1}{8^n+1}$ diverges; $b_n=(\frac{5}{8}{)}^n$; Limit value $=$

The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5^n+1}{8^n+1}$ diverges ; $b_n=(\frac{8}{5}{)}^n$; Limit value $=$

The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5^n+1}{8^n+1}$ converges; $b_n=(\frac{8}{5}{)}^n$; Limit value $=1$

The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5^n+1}{8^n+1}$ converges; $b_n=(\frac{5}{8}{)}^n$; Limit value $=1$