Proof by induction, puzzles by answer

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    Induction Proof
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Discussion Overview

The discussion revolves around a proof by induction question, specifically focusing on the transition from the expression 2^(k+1) to 2^(k+2). Participants are seeking clarification on the mathematical steps involved in this transformation.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the transition from 2^(k+1) to 2^(k+2) and requests clarification.
  • Another participant suggests that more background information is needed to address the question effectively.
  • A third participant notes that an image linked in the discussion did not load properly, hindering the ability to respond accurately.
  • A later reply attempts to clarify the transformation by stating that multiplying 2^(k+1) by 2 results in 2^(k+2), explaining that this is due to raising the exponent by 1.
  • Another participant reiterates the multiplication of 2^(k+1) by 2, confirming the resulting expression as 2^(k+2).

Areas of Agreement / Disagreement

The discussion shows some participants agreeing on the mathematical reasoning behind the transformation, while others express confusion and seek further clarification. No consensus is reached on the overall understanding of the proof.

Contextual Notes

Participants have not provided sufficient background or context regarding the specific proof by induction being discussed, which may limit understanding. Additionally, the lack of a properly linked image may contribute to the confusion.

MegaDeth
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Ok, so there's this proof by induction question. I looked at the answer for it but I don't understand it.

TuXle.jpg


How does it get from being 2^(k+1) to being 2^(k+2)?
 
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You need to provide a little more background into your question, I think.
 
Your image did not link properly so it is impossible to answer your question.
 
MegaDeth said:
How does it get from being 2^(k+1) to being 2^(k+2)?
2^{k+1}(k-1+k+1) = 2^{k+1}(2k) = 2^{k+2}k
 
you got [2^(k+1)](2k).

multiply 2^(k+1) by two, that is raising your exponent by 1. Hence 2^(k+2)
 
Last edited:

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