1. The problem statement, all variables and given/known data Determine whether the series converges or diverges. [tex]\sum[/tex](1+5^n) / (1+6^n) 2. Relevant equations limit comparison test, or just the comparison test. 3. The attempt at a solution [attempt #1] I have a couple of ways of trying to proves this. 1) (1+5^n) / (1+6^n) < (1 + 5^n) / 6^n = (1/6)^n + (5/6)^n , which converges to 1/5 + 5 = 26/5 so since the series is bounded by 0 <= (1+5^n)/(1+6^n) <=26/5 it converges? This might not necessarily be true because a function might fluctuate between those points until infinity, but I think that only cosine have this property. Thus this series converges. [attempt # 2] (1+5^n) / (1+6^n) = 1 / (1+6^n) + (5/6)^n I know that (5/6)^n converges to 5, so = 1/(1+6^n) + 5 now I apply the comparison test to 1/(1+6^n) 1/(1+6^n) < 1/(6^n), and this converges to 0.2 so , [0<= 1/(1+6^n) <= 0.2 ] + 5 so it converges since 1/(1+6^n) is bounded. Either 1 right?