Practice Exam 4

# 4 a 3 n ln n 1 n1 b n2 n1 n2 c sin n

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Unformatted text preview: t, or divergent. ∞ 4 (a) 3 n (ln n) √ 1 + n−1 (b) n2 n=1 n=2 ∞ ∞ (c) sin n − 2 n2 n=1 ∞ (d) n4 + 2n − 1 n5 + 3n2 − 20 n=1 ∞ (e) 1 e n +1 n3 n=1 ∞ (f) n=1 ∞ (g) n=1 ∞ (h) (−1) n 4n 5n + 1 ∞ n=1 ∞ (−1) n 4n (2n + 1)! n3 e−n (j) n=1 ∞ n (−1) √ n n=1 ∞ (l) n=1 ∞ (m) n 2·n 3n n=1 (i) (k) 4 n+1 4n (n!) 2 n1 (−1) √ n n n=1 ∞ 6. Estimate the sum of the series n=1 (−1) n n to within 0.01 n4 + 1 7. Determine the number of terms necessary to estimate the sum of the following series to within 1 × 10−6 ∞ (a) n=1 ∞ (b) n=1 (−1) n (−1) n 3 n2 2n n! ∞ 8. Find all real values of x for which the series n=1 (−1) n xn converges. n · 4n...
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## This document was uploaded on 03/11/2014 for the course MATH 262 at Minnesota State University Moorhead .

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