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Unformatted text preview: x , (3) lim x →∞ ln( x + 1)-ln x. 1 2 CALCULUS 153: MIDTERM 1 Problem 4 (8 points) . State the ± – K deﬁnition of lim n →∞ a n = L . Problem 5 (14 points) . Prove that if a n → L and b n → M then a n + b n → L + M . Problem 6 (20 points) . Please answer true or false (you do not need to justify your answer). (1) If M is an upper bound for S , and M ∈ S , then M is the least upper bound for S . (2) The least upper bound of a set S must be contained in S . (3) The least upper bound of a set of irrational numbers must be irrational. (4) A sequence that is bounded and increasing must converge. (5) If a n + b n converges then both a n and b n must converge....
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This note was uploaded on 04/07/2008 for the course MATH 153 taught by Professor Masson during the Fall '07 term at UChicago.
- Fall '07