1. The problem statement, all variables and given/known data Hey, I need some help with these three problems which have to do with the convergence or divergence of the series. If you can, please let me know how you solved each problem including which kind of test you used for example. Anyways, here are the problems: 1) [tex]\Sigma[/tex] (1)/(n + n*(cosn)^2), from 1 to infinity 2) [tex]\Sigma[/tex] (5^n)/(3^n + 4^n), from 1 to infinity 3) [tex]\Sigma[/tex] (n*sin(1/n)), from 1 to infinity Thank you in advance for your help. The soonest you can reply to me, the best because I need these answers soon! :) 2. Relevant equations N/A. 3. The attempt at a solution For the first one, I tried to use the integral test but I don't really think that this can be the best approach. For the second one, I tried using the ratio test but I don't know how to factor out the terms I need to in order the result of the limit. For the third one, I got that the series diverges because at n -> infinity, sin(1/n) ~ 1/n. Therefore, when I substitute sin(1/n) for 1/n and use the nth term test I get that the limit as n approaches infinity = 1 which is not 0, therefore, according to the nth term test the series diverges.