MAT 127: Calculus C, Fall 2009Mini-Quiz:convergence/divergence of sequences/seriesDO NOT TURN THIS PAGE OVER YETThis mini-quiz is for practice only. It will not be graded or even collected.On the next page, you will find 5 sequences and 5 series. You need to determine whether each ofthem converges and circle YES or NO, without justifying your answer (but keep a reason in mind).A similar problem on the final exam will contain a total of 5 sequences and series.You have 10 minutes to answer all 10 questions.Taking about 10 minutes on the analogous, 5-question, problem on the final should be ok (thiswould be one point per minute, which is what you need to average). Thus, you are being asked tocomplete the mini-quiz at about 2 times the pace needed for the final exam; this is because you donot have 7 other problems to deal with and are under less pressure. However, please do not rushthrough the analogous problem on the final.Determine whether each of the following sequences or series converges or not. In each case, clearlycircle either YES or NO, but not both.(a) the sequence an=(−1)n−1nn2+ 1YES NO(b) the sequence an= 1 + cos(2/n) YES NO(c) the sequence an= n cos n YES NO(d) the sequence an= (−1)nnn + 1YES NO(e) the sequence an=sin 2n1 +√nYES NO(f) the series∞Xn=1n√n2+ 1YES NO(g) the series∞Xn=14 + 3n2nYES NO(h) the series∞Xn=17nn!YES NO(i) the series∞Xn=1sin n2nYES NO(j) the series∞Xn=1(−1)nnn2+ 1YES
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