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Unformatted text preview: k is: (A) 16 15 . (B) 13 16 . (C) 12 15 . (D) 17 16 . (E) divergent. 9) lim x → + 3 x sin( x ) = (A) 3 e . (B) 3. (C) 6 e . (D) 6. (E) 3 e . 10) A sequence is deFned by a n +1 = 1 / (1 + a n ), a 1 = 1, n ≥ 1. Assuming this sequence is convergent, its limit is: (A) √ 31 2 . (B)√ 51 2 . (C) 1. (D) 1 2 . (E) √ 51 2 . 11) A sequence a k ( k ≥ 1) with partial sums s n ( n ≥ 1) satisFes a k > 0 and s n ≤ 5 for all k and n . Which of the following statements may be false ? (A) s n is increasing. (B) s n is bounded above. (C) a k is monotonic. (D) ∞ s k =1 a k converges. (E) s n is bounded below. 12) If ∞ s k =2 Q p 1 5 P k = 1 12 , then the value of the constant Q must be: (A) 5 3 . (B) 3 2 . (C) 4 9 . (D) 1 6 . (E) 2 5 ....
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 Spring '07
 Sadler
 Limits, Summation, Order theory, Monotonic function

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