Discover a closed formula for the following recursive sequence. Prove your formula by mathematical induction. Fill in the chart below to aid your discovery. Define a recursive sequence as а, 3D 1, а, 3 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Mathematical Reasoning
Writing and Proof:

Discover a closed formula for the following recursive sequence.
Prove your formula by mathematical induction. Fill in the chart
below to aid your discovery.
Define a recursive sequence as
а, - 1, а, - 2
а
•a, pz1
= A
p+2
p+1
n
а
n
1
1
a,
2
1
a2
=
1
a, =
4
3
2
3
as
8
4
=
7
13
а,
8
21
6.
az
9.
34
7
a, =
3.
Transcribed Image Text:Discover a closed formula for the following recursive sequence. Prove your formula by mathematical induction. Fill in the chart below to aid your discovery. Define a recursive sequence as а, - 1, а, - 2 а •a, pz1 = A p+2 p+1 n а n 1 1 a, 2 1 a2 = 1 a, = 4 3 2 3 as 8 4 = 7 13 а, 8 21 6. az 9. 34 7 a, = 3.
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