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Ing recursively defined sequence. the f = f-1+ 2*, for each integer k 2 2 f1 = 1 Fill in the blanks to use iteration to guess an explicit formula for the sequence. f = 1 f2 = f, +2 f3 = f, +2 f4 = f3+2 = 1 + 2 = 1 + 22 + 2 = 1 + 22 + 23 + 2 Guess: f, = 1 + 22 + 23 + 24 + . + When Theorem 5.2.2 is used to simplify this expression, the result is - 1 f, = 2, 2 1 and, when this expression is simplified, the result is f - 3 for every integer n 2 1.

Ing recursively defined sequence. the f = f-1+ 2*, for each integer k 2 2 f1 = 1 Fill in the blanks to use iteration to guess an explicit formula for the sequence. f = 1 f2 = f, +2 f3 = f, +2 f4 = f3+2 = 1 + 2 = 1 + 22 + 2 = 1 + 22 + 23 + 2 Guess: f, = 1 + 22 + 23 + 24 + . + When Theorem 5.2.2 is used to simplify this expression, the result is - 1 f, = 2, 2 1 and, when this expression is simplified, the result is f - 3 for every integer n 2 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following recursively defined sequence. fk = f-1+2", for each integer k 2 2 f = 1 Fill in the blanks to use iteration to guess an explicit formula for the sequence. f1 = 1 2 = r, + 2- 3 =f, + 2- f4 = f3 + 2 = 1 + 2 = 1 + 22 + 2 = 1 + 22 + 23 + 2 Guess: f, = 1 + 22 + 23 + 24. + ... + When Theorem 5.2.2 is used to simplify this expression, the result is 1 - 2, 2 1 and, when this expression is simplified, the result is f 3 for every integer n 2 1.
Transcribed Image Text:Consider the following recursively defined sequence. fk = f-1+2", for each integer k 2 2 f = 1 Fill in the blanks to use iteration to guess an explicit formula for the sequence. f1 = 1 2 = r, + 2- 3 =f, + 2- f4 = f3 + 2 = 1 + 2 = 1 + 22 + 2 = 1 + 22 + 23 + 2 Guess: f, = 1 + 22 + 23 + 24. + ... + When Theorem 5.2.2 is used to simplify this expression, the result is 1 - 2, 2 1 and, when this expression is simplified, the result is f 3 for every integer n 2 1.
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