1) Determine whether the infinite series ∞ Sigma (k^2-1) / (3k^4 + 1) k=0 converges or diverges. [My immediate thought was to use the "limit comparsion test", but this test requires all terms to be positive. However, the first term (put k=0) is definitely negative...what should I do? Can I still use the limit comparsion test, and if not, what other tests can I use?] 2) Evaluate lim [t^2 - t^3 sin(1/t)] t->∞ [When I direct substitute, I get ∞-∞*0, and I have no clue how to solve this problem...any hints?] Thank you for your help!