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Chap10evenanswers(2)

Chap10evenanswers(2) - MATH 1042 Section 10.1 12 a)11 38 0...

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MATH 1042 Chapter 10 Even Homework Answers Section 10.1 12) a )11 b )64 c )28 d ) - 40 14) 3 2 22) 1 38) 0 60) Diverges Section 10.2 4) S 2 = - 1 / 2; S 4 = - 7 / 12; S 6 = - 37 / 60 12) S n = 0 if n is even and S n = 1 if n is odd, so the sequence of partial sums, and hence the series, diverges. 16) Since lim n →∞ cos (1 /n ) = cos 0 = 1 = 0, the series diverges by the Divergence Test. 20) 11 8 24) 1 e - 1 26) 35 3 28) 4 30) 7 15 32) b) and c) Extra Problems: a) 4 b) Diverges c) 9 10 Section 10.3 10) Converges (Use Integral Test) 18) The second inequality is useful: the first will give that your terms are smaller than terms of a divergent series - that doesn’t help you; the second inequality gives the terms are smaller than terms of a convergent series which allows you to conclude convergence. 30) Converges (Use ln n < n and compare to 1 n 2 ) 36) Diverges (Limit comparison with 1 n 1 / 2 ) 38) Coverges (Limit comparison with 1 n 2 ) 40) Converges (Limit Comparison with 1 n 3 / 2 ) 50) Converges (Compare to 1 n 2 ) 52) Converges (geometric with r = 1 /e ) 54) Converges (Limit Comparison with 1 n 2 ) 56) Diverges (Test for Divergence)
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Section 10.4
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