Consider the sequence defined as follows, 2 8-1 Sk = = " $1 ke Z, k>2 = 1 = Find an explicit formula, S (n), for the sequence (in can be piecewise explicit) by using the process of iteration (expand looking for patterns, guess, check). you must show the iterative expansion of 81, 82, 83,, 87 and indicate how it reveals a pattern.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the sequence defined as follows,
Sk =
2
87-1
"
81
ke Z, k>2
1
1
Find an explicit formula, S (n), for the sequence (in can be piecewise explicit) by using
the process of iteration (expand looking for patterns, guess, check).
you must show the iterative expansion of 81, 82, 83,..., 87 and
indicate how it reveals a pattern.
You do not need to prove your explicit formula is correct, but you must show that it
evaluates to the same number that the sequence produces at k = 8.
That is, you must show an evaluation of sg by definition and by use of your formula
S (8) at k = 8.
Transcribed Image Text:Consider the sequence defined as follows, Sk = 2 87-1 " 81 ke Z, k>2 1 1 Find an explicit formula, S (n), for the sequence (in can be piecewise explicit) by using the process of iteration (expand looking for patterns, guess, check). you must show the iterative expansion of 81, 82, 83,..., 87 and indicate how it reveals a pattern. You do not need to prove your explicit formula is correct, but you must show that it evaluates to the same number that the sequence produces at k = 8. That is, you must show an evaluation of sg by definition and by use of your formula S (8) at k = 8.
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