Who wants to be a millionaire II

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Who wants to be a millionaire? (II)
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Question 1 for 100 GU

• The sequence
• converges and its limit is
• A) 0
• B) 1
• C) 2
• D) e

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Question 2 for 200 GU

• The harmonic series
• A) converges to 1
• B) converges to 2
• C) converges to ln 2
• D) diverges

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Question 3 for 300 GU

• The sum
• A) equals to 10
• B) equals to 14
• C) equals to n(n 1)/2
• D) diverges

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Question 4 for 500 GU

• The power series
• converges for all x, and its sum is
• A) sin x
• B) cos x
• C) ex
• D) ln(1 x)

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Question 5 for 1,000 GU

• The linearization of the function
• f(x) sin x
• at x ? is given by
• A) L(x) cos x
• B) L(x) x2 ? ?
• C) L(x) ? ? x (the only line)
• D) L(x) 1/x

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You won 1000 GU!
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Question 6 for 2,000 GU

• The sequence
• converges and its limit is
• A) 0
• B) ?1 (by LHopital)
• C) 2
• D) 3

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Question 7 for 4,000 GU

• The power series
• converges when ?1 lt x lt 1, and its sum is
• A) 1 x
• B) 1 ? x
• C) 1/(1 ? x) (Geometric with a 1,
  r x)
• D) 1/(1 x)

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Question 8 for 8,000 GU

• The series
• converges and its sum is
• A) 1
• B) 2 (2/3)/(1 ? 2/3)
• C) 3
• D) 4

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Question 9 for 16,000 GU

• The alternating series
• A) converges absolutely
• B) converges conditionally
• C) diverges
• D) none of the above

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Question 10 for 32,000 GU

• The series
• A) converges absolutely (See Lecture 5,
  Slide 17.)
• B) converges conditionally
• C) diverges
• D) none of the above

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You won 32,000 GU!
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Question 11 for 64,000 GU

• The series
• A) converges absolutely
• B) converges conditionally
• C) diverges (limnan e2 ? 0)
• D) none of the above

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Question 12 for 125,000 GU

• The series
• A) converges to 2 (difference of two
  geometric series)
• B) converges to 1
• C) converges to 1/4
• D) diverges

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Question 13 for 250,000 GU

• The series
• A) converges absolutely
• B) converges conditionally
• C) diverges (apply the Root Test)
• D) none of the above

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Question 14 for 500,000 GU

• The series
• A) converges absolutely (Compare the series
  of absolute values to 1/((n(lnn)2), which
  converges using the integral test.)
• B) converges conditionally
• C) diverges
• D) none of the above

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Question 15 for 1,000,000 GU

• The series
• A) converges to e
• B) converges to e ? 1 (Use the Maclaurin
  series for ex when x 1)
• C) converges to e?1
• D) converges to e?1 ? 1

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You won 1,000,000 GU!
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• Thank you for listening.
• Wafik