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# T4Solutions.pdf

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Carleton University

Mathematics

MATH 1005

Ida Toivonen

Fall

Description

MATH 1005B
Test 4 Solutions
March 20, 2012
[Marks] Questions 1-4 are multiple choice. Circle the correct answer. Only the answer will be marked.
∞ n+1
[3] 1. The sum of the series is
3n
n=0
2 4
(a) 3 (b) (c) (d) 1 (e) 6
3 3
Answer:(e)
[3] 2. Which of the following series converge(s)?
1 ∞ 4n+1 ∞ 6n
(i) (ii) (iii)
2n 5n 5n
n=0 n=0 n=0
(a) (i), (ii) and ((b) (i) and (i(c) (i) and (ii(d) (ii) and (ii(e) (i)
Answer:(b)
[3] 3. Which of the following series converge(s)?
∞ ∞ n ∞
1 (−1) 1
(i) √ (ii) √ (iii) √
n=1 n n=1 n n=1n n
(a) (i), (ii) and ((b) (i) and (i(c) (i) and (ii(d) (ii) and (ii(e) (iii)
Answer: (d)
[3] 4. Which of the following series converge(s) absolutely?
n ∞ n
(i) (−1) (ii) (−1) (iii) n
nln(n) n2 n +1
n=2 n=0 n=0
(a) (i), (ii) and ((b) (i) and (i(c) (ii) (d) (ii) and (ii(e) (iii)
Answer:(c)
∞ 2
n +2 n +1
[3] 5. Determine whether or not the series 4 converges. Justify your answer.
n=1 n +1
Solution:
n +2 n +1
lim √ =1 ▯=0 ⇒ the series diverges by th-term test.
n→∞ n +1
n
[3] 6. Determine whether or not the series4 converges. Justify your answer.
2n
n=0
Solution:
3 +4 3n 3 n

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