Help with Mathematical Induction

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Homework Help Overview

The discussion revolves around proving a statement related to divisibility using mathematical induction, specifically that \( (2^{(n+1)} + 9(13^n)) \) divides by 11 for all positive integers.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the validity of the initial statement and discuss the structure of mathematical induction, including establishing a base case and assuming the proposition for \( n = k \) to show it holds for \( n = k+1 \.

Discussion Status

There is an ongoing exploration of the problem with participants questioning the truth of the initial statement and discussing the necessary steps for induction. Some guidance has been offered regarding the use of modular arithmetic to assist in the proof.

Contextual Notes

Participants express uncertainty about where to begin and the original poster indicates a lack of direction in their initial attempt.

SeattleScoute
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Homework Statement



Prove by matematical induction that (2^(n+1)+9(13^n)) divides by by 11 for all positive intergers


Homework Equations





The Attempt at a Solution



I really have no idea where to start...
 
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The problem outright tells you a place to start!
 
Is P1 true? If so, then if I say Pk is true is Pk+1 also true?
 
jegues said:
Is P1 true? If so, then if I say Pk is true is Pk+1 also true?
Are you also SeattleScoute?

That's basically what is needed. Establish a base case. Assume the proposition is true for n = k. Show that P(k) being true implies that P(k+1) is also true.
 
Are you also SeattleScoute?

No I'm not, I thought I'd help :S
 
you may use modular arithmetic to lighten your job .
 

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