HW 10 key

HW 10 key - Miller Kierste – Homework 10 – Due Apr 4...

This preview shows pages 1–3. Sign up to view the full content.

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.

Unformatted text preview: Miller, Kierste – Homework 10 – Due: Apr 4 2007, 3:00 am – Inst: Gary Berg 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find a formula for the general term a n of the sequence n 1 , 6 , 11 , 16 , ... o assuming that the pattern of the first few terms continues. 1. a n = 4 n- 3 2. a n = n + 5 3. a n = 5 n- 4 correct 4. a n = n + 4 5. a n = 6 n- 5 Explanation: In the sequence n 1 , 6 , 11 , 16 , ... o each term is larger than the preceding one by 5, so a n = a 1 + d ( n- 1) = 1 + 5( n- 1) . Consequently, a n = 5 n- 4 . keywords: 002 (part 1 of 1) 10 points Find a formula for the general term a n of the sequence n 1 ,- 5 4 , 25 16 ,- 125 64 , ... o assuming that the pattern of the first few terms continues. 1. a n = ‡- 5 4 · n- 1 correct 2. a n = ‡- 4 5 · n- 1 3. a n =- ‡ 5 4 · n 4. a n =- ‡ 6 5 · n 5. a n =- ‡ 4 5 · n 6. a n = ‡- 6 5 · n- 1 Explanation: In the sequence n 1 ,- 5 4 , 25 16 ,- 125 64 , ... o each term is- 5 4 times the preceeding one, i.e. , a n = ‡- 5 4 · a n- 1 . Consequently, a n = ‡- 5 4 · n- 1 since a 1 = 1. keywords: sequence, exponential 003 (part 1 of 1) 10 points Determine if the sequence { a n } converges, and if it does, find its limit when a n = 4 n 5- 2 n 3 + 5 3 n 4 + 4 n 2 + 5 . 1. limit = 1 2. limit = 4 3 Miller, Kierste – Homework 10 – Due: Apr 4 2007, 3:00 am – Inst: Gary Berg 2 3. limit = 0 4. the sequence diverges correct 5. limit =- 1 2 Explanation: After division by n 4 we see that a n = 4 n- 2 n + 5 n 4 3 + 4 n 2 + 5 n 4 . Now 2 n , 5 n 4 , 4 n 2 , 5 n 4-→ as n → ∞ ; in particular, the denominator converges and has limit 3 6 = 0. Thus by properties of limits { a n } diverges since the sequence { 4 n } diverges. keywords: 004 (part 1 of 1) 10 points Determine whether the sequence { a n } con- verges or diverges when a n = 8 n 2 4 n + 1- 2 n 2 + 7 n + 1 , and if it does, find its limit 1. limit = 1 2 2. limit = 0 3. the sequence diverges 4. limit = 3 4 5. limit = 3 2 correct Explanation: After bringing the two terms to a common denominator we see that a n = 8 n 3 + 8 n 2- (4 n + 1)...
View Full Document

{[ snackBarMessage ]}

Page1 / 7

HW 10 key - Miller Kierste – Homework 10 – Due Apr 4...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online