MA 2733 Midterm: MATH 2733 MSState OES F13 2A
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A correct answer is worth 2 points, a blank space is worth 0 points, and a wrong answer is worth -2 points. (your total on this problem will be rounded up to zero if necessary. ) (a) t. The sequence an = 4 3n can be expressed recursively as a1 = 12, an = 3an 1 for n > 1. (b) f. Xn=1 an = l means that lim n m. While this looks somewhat similar to the de nition of a series, it is nonsense. 2 n), we have lim n an = 0. Since the sequence is 1, 0, 1, 0, 1, 1, . , and in particular is both 1 in- Nitely often and 1 in nitely often. (d) t. 1 n sin(n2), we have lim n an = 0. By the squeeze theorem, since 0 1 n sin(n2) 1 n . (e) f. The acceleration vector of any particle is orthogonal to its velocity vector.
