T4Solutions

# T4Solutions - MATH 1005A Test 4 Solutions[Marks Questions 1...

This preview shows pages 1–2. Sign up to view the full content.

MATH 1005A Test 4 Solutions March 23, 2010 Questions 1 and 2 are multiple choice. Circle the correct answer. Only the answer will be [Marks] marked. 1. Which of the following series converge(s)? (i) 1 X n =0 3 2 n (ii) 1 X n =1 ( ¡ 1) n n (iii) 1 X n =1 1 n [3] (a) All (b) (i) and (ii) (c) (i) and (iii) (d) (ii) and (iii) (e) None Solution: (b) 2. Which of the following series converge(s)? (i) 1 X n =1 2 n n n (ii) 1 X n =1 n n n ! (iii) 1 X n =1 3 n ¢ 2 n [3] (a) All (b) (i) and (ii) (c) (i) and (iii) (d) (ii) and (iii) (e) None Solution: (c) 3. Determine whether the given series converges absolutely, converges conditionally, or diverges. Justify your answer. (a) 1 X n =1 ( ¡ 1) n n p n 2 +1 [4] Solution: The series diverges by the n th -term test since lim n !1 a n 6 =0(doesnotexist). (b) 1 X n =1 ( ¡ 1) n n 2 +1 [4] Solution: The series converges absolutely by the comparison test since ¯ ¯ ¯ ¯ ( ¡ 1) n n 2 +1 ¯ ¯ ¯ ¯ = 1 n 2 +1 1 n 2 and 1 X n =1 1 n 2 converges since it is a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 04/14/2010.

### Page1 / 2

T4Solutions - MATH 1005A Test 4 Solutions[Marks Questions 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online