M408L_HW11 - hyun(hh7953 – HW11 – gogolev –(57440 1...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: hyun (hh7953) – HW11 – gogolev – (57440) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine if the sequence { a n } converges when a n = 1 n ln parenleftbigg 5 6 n + 5 parenrightbigg , and if it does, find its limit. 1. limit = ln 5 6 2. limit = 0 correct 3. limit = − ln 6 4. the sequence diverges 5. limit = ln 5 11 Explanation: After division by n we see that 5 6 n + 5 = 5 n 6 + 5 n , so by properties of logs, a n = 1 n ln 5 n − 1 n ln parenleftbigg 6 + 5 n parenrightbigg . But by known limits (or use L’Hospital), 1 n ln 5 n , 1 n ln parenleftbigg 6 + 5 n parenrightbigg −→ as n → ∞ . Consequently, the sequence { a n } converges and has limit = 0 . 002 10.0 points Find a formula for the general term a n of the sequence { a n } ∞ n =1 = braceleftBig 3 , 8 , 13 , 18 , . . . bracerightBig , assuming that the pattern of the first few terms continues. 1. a n = 6 n − 3 2. a n = 4 n − 1 3. a n = n + 4 4. a n = n + 5 5. a n = 5 n − 2 correct Explanation: By inspection, consecutive terms a n − 1 and a n in the sequence { a n } ∞ n =1 = braceleftBig 3 , 8 , 13 , 18 , . . . bracerightBig have the property that a n − a n − 1 = d = 5 . Thus a n = a n − 1 + d = a n − 2 + 2 d = . . . = a 1 + ( n − 1) d = 3 + 5( n − 1) . Consequently, a n = 5 n − 2 . keywords: 003 10.0 points Find a formula for the general term a n of the sequence { a n } ∞ n =1 = braceleftBig 1 , − 3 4 , 9 16 , − 27 64 , . . . bracerightBig , assuming that the pattern of the first few terms continues. 1. a n = parenleftBig − 4 3 parenrightBig n − 1 hyun (hh7953) – HW11 – gogolev – (57440) 2 2. a n = parenleftBig − 4 5 parenrightBig n − 1 3. a n = − parenleftBig 4 5 parenrightBig n 4. a n = parenleftBig − 3 4 parenrightBig n − 1 correct 5. a n = − parenleftBig 4 3 parenrightBig n 6. a n = − parenleftBig 3 4 parenrightBig n Explanation: By inspection, consecutive terms a n − 1 and a n in the sequence { a n } ∞ n =1 = braceleftBig 1 , − 3 4 , 9 16 , − 27 64 , . . . bracerightBig have the property that a n = ra n − 1 = parenleftBig − 3 4 parenrightBig a n − 1 . Thus a n = ra n − 1 = r 2 a n − 2 = . . . = r n − 1 a 1 = parenleftBig − 3 4 parenrightBig n − 1 a 1 . Consequently, a n = parenleftBig − 3 4 parenrightBig n − 1 since a 1 = 1. keywords: sequence, common ratio 004 10.0 points Determine if the sequence { a n } converges, and if it does, find its limit when a n = 6 n 5 − 3 n 3 + 1 8 n 4 + n 2 + 1 ....
View Full Document

{[ snackBarMessage ]}

Page1 / 8

M408L_HW11 - hyun(hh7953 – HW11 – gogolev –(57440 1...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online