CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
5th Edition
ISBN: 9780133320381
Author: Finney
Publisher: SAVVAS L
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sum Sn. (b) Use (a) to determine whether the series is convergent or divergent. 8 (5) Decide whether each of the following statements is true or false. If a statement is true, explain why. If a statement is false, provide specific examples of ak and Σb for k=1 which the statement is false. Σ (a) If 5 am is a series such that ak a k=1 1 k² < ak for all k, then (d) If ak k=1 (b) If ak is a series such that 0 < a
+oo en +2 Let S. be the n-th partial sum of the series S = ak - 3e" + n? n100 +oo a. Does the series > ak converge? If it is convergent, find its sum. k=1 b. Find lim ak: k→+∞
6. Let a be a real number. Consider the series where an = cos(na): 2n +1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally.
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