- #1
kingwinner
- 1,270
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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!
∞
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!