1. The problem statement, all variables and given/known data Use the Limit Comparison Test to determine if the series converges or diverges: Ʃ (4/(7+4n(ln^2(n))) from n=1 to ∞. (The denominator, for clarity, in words is: seven plus 4n times the natural log squared of n.) 2. Relevant equations Limit Comparison Test: Let Σa(n) be the original series, and Σb(n) be the comparison series. 1. If the lim(n->∞) a(n)/b(n) is a positive number, but not ∞, then a(n)'s convergence/divergence is the same as b(n)'s. 2. If the lim(n->∞) a(n)/b(n) = 0, then if b(n) is convergent, so is a(n), but if b(n) is divergent, the result is inconclusive. 3. If the lim(n->∞) a(n)/b(n) = ∞, then if b(n) is divergent, so is a(n), but if b(n) is convergent, the result is inconclusive. 3. The attempt at a solution I need to use a p-series to determine if this series diverges or converges, but every p-series I have tried gives the result that makes it inconclusive. Here is the issue: When I make b(n) = 1/n (p-series that diverges), I get a limit of 0, which is inconclusive (via case 2). When I make b(n) = 1/(n^2) (p-series that converges), I get a limit of ∞, which is inconclusive (via case 3). No matter what p-series I try, I get an inconclusive case... Can anyone find a comparison p-series that (using the Limit Comparison Test) works?? My instructor said a p-series will work, but everything I try does not. Please show all steps. Thank you!