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

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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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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