1. For nENº, 12" – 5ª is divisible by 7 (Note: N° =NU{0}). %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Please answer the question in the screenshot about induction. Please give a detailed explanation. 

Give a carefully worded proof for the following statement.
Prove the following statement with induction (Please follow the proper format for
inductive proof and give sufficient detail for clarity and completeness).
1. For nENº, 12" – 5" is divisible by 7 (Note: N° =NU{0}).
2. Prove that 2" + 1 < 3ª for every positive integer n.
1
3
n
3. If nEN, then
1
(n+1)!
...
-
2!
3!
4!
(n+1)!
Transcribed Image Text:Give a carefully worded proof for the following statement. Prove the following statement with induction (Please follow the proper format for inductive proof and give sufficient detail for clarity and completeness). 1. For nENº, 12" – 5" is divisible by 7 (Note: N° =NU{0}). 2. Prove that 2" + 1 < 3ª for every positive integer n. 1 3 n 3. If nEN, then 1 (n+1)! ... - 2! 3! 4! (n+1)!
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