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Friday, March 1 Clicker Questions Clicker Question 1 Trying to make a sequence converge Let {an } be a sequence that we hope converges. Each of these statements might or might not be true: I. Every term is larger than the previous one: a1 < a2 < a3 < · · · . II. All of the terms are real numbers between 1 and 8. Which statement(s), if true, would always force {an } to converge? A. either one of I or II is enough to make {an } converge B. I makes {an } converge, regardless of whether II is true C. II makes {an } converge, regardless of whether I is true D. nether I nor II makes {an } converge by itself, but together I and II make {an } converge E. even I and II together don’t make {an } converge Clicker Question 2 Almost a geometric series Calculate A. B. C. D. E. 7 9 9 9 9 + + + + + ···. 10 100 10,000 1,000,000 100,000,000 87 110 4 5 70 99 1 11 none of the above From our formula ∞ X 9 7 1 r−1 + 10 100 100 i=1 7 9/100 + 10 1 − 1/100 7 9 = + 10 100 − 1 7 1 = + . 10 11 =