Calculus II Name:
Ver 1 Student ID:
Quiz 4
Apr. 11, 2007
1. (5pts) Determine if the sequence converges or diverges. If it converges, find the limit.
an= 2n2+ n n2− 3
2. (7pts)Determine if the series converges or diverges.
∑∞ n=1
( 1 3k + k)
3. . (8pts) Determine convergence or divergence of the series.
∑∞ k=1
k + 2 k3+ k2+ 3
4. (0pt) Achilles and the tortoise-“You can never catch up.”
“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.”
(Aristotle Physics VI:9, 239b15)
Being very fast, Greek hero Achilles gives the Tortoise a head start. But that would be a big mistake, claims Zeno, for then Achilles could never catch up. Why not? The proof is that by the time Achilles reaches the Tortoises starting point S1, the Tortoise will have moved a little to S2, but then by the time Achilles reaches S2 the Tortoise will have moved on to S3, but then by the time ...
