Math 1B Section 107 Quiz #7Thursday, 11 October 2007GSI: Theo Johnson-Freydhttp://math.berkeley.edu/∼theojfName:1. True or False (1 pt each) For each of the following statements, decide if it is trueor false. You do not need to show work: I will grade only your answers.(a) Let’s say 0 ≤ an≤ bn, andP∞n=1an= A andP∞n=1bn= B. If A = B, thenan= bnfor every n.(b) If 0 ≤ an≤ f(n), where f(x) is a continuous decreasing function on x ∈ [1, ∞),such thatR∞1f(x) dx converges, thenP∞n=1anconverges.(c) If 0 ≤ an≤ π/2 andP∞n=1sin(an) diverges, thenP∞n=1andiverges.1For the next two questions, use either the Limit Comparison Test or the Integral Testto determine if the series converges or diverges. Be sure to check that the series satisfiesthe conditions necessary for the test.2. (3 pts)∞Xn=1arctan(n)n2− ln(n)3. (4 pts)∞Xn=31n ln n ln(ln
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