# REVIEW3 - momin (rrm497) Review 3 cheng (58520) 1 This...

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: momin (rrm497) Review 3 cheng (58520) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine whether the sequence { a n } con- verges or diverges when a n = ( 1) n 1 n n 2 + 5 , and if it converges, find the limit. 1. converges with limit = 1 5 2. converges with limit = 0 correct 3. converges with limit = 1 5 4. converges with limit = 5 5. sequence diverges 6. converges with limit = 5 Explanation: After division, a n = ( 1) n 1 n n 2 + 5 = ( 1) n 1 n + 5 n . Consequently, | a n | = 1 n + 5 n 1 n . But 1 /n 0 as n , so by the Squeeze theorem, lim n | a n | = 0 . But | a n | a n | a n | , so by the Squeeze theorem again the given sequence { a n } converges and has limit = 0 . keywords: 002 10.0 points Determine if the sequence { a n } converges when a n = 7 n 2 (2 n 1)! (2 n + 1)! , and if it converges, find the limit. 1. converges with limit = 7 2 2. converges with limit = 2 7 3. converges with limit = 4 7 4. does not converge 5. converges with limit = 7 4 correct Explanation: By definition, m ! is the product m ! = 1 2 3 . . . m of the first m positive integers. When m = 2 n 1, therefore, (2 n 1)! = 1 2 3 . . . (2 n 1) , while (2 n + 1)! = 1 2 3 . . . (2 n 1)2 n (2 n + 1) . when m = 2 n + 1. But then, 7 n 2 (2 n 1)! (2 n + 1)! = 7 n 2 2 n (2 n + 1) 7 4 as n . Consequently, the given sequence converges with limit = 7 4 . momin (rrm497) Review 3 cheng (58520) 2 003 10.0 points Determine whether the infinite series summationdisplay n =1 ( n + 1) 2 n ( n + 2) converges or diverges, and if converges, find its sum. 1. converges with sum = 1 4 2. converges with sum = 1 3. converges with sum = 1 2 4. diverges correct 5. converges with sum = 1 8 Explanation: By the Divergence Test, an infinite series n a n diverges when lim n a n negationslash = 0 . Now, for the given series, a n = ( n + 1) 2 n ( n + 2) = n 2 + 2 n + 1 n 2 + 2 n . But then, lim n a n = 1 negationslash = 0 . Consequently, the Divergence Test says that the given series diverges . keywords: infinite series, Divergence Test, ra- tional function 004 10.0 points Determine whether the series summationdisplay n = 3 ( 1) n +2 5 n ln n converges conditionally, converges absolutely, or diverges. 1. series converges absolutely 2. series converges conditionally correct 3. series diverges Explanation: The given series can be rewritten as summationdisplay n =3 ( 1) n +2 5 n ln n = 5 summationdisplay n =3 ( 1) n f ( n ) , where f ( x ) = 1 x ln x = ( x ln x ) 1 ....
View Full Document

## REVIEW3 - momin (rrm497) Review 3 cheng (58520) 1 This...

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

View Full Document
Ask a homework question - tutors are online