Understanding Induction: Solving a Challenging Step

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Homework Help Overview

The discussion revolves around understanding a specific step in an induction proof related to a mathematical expression. Participants are exploring the nuances of the induction process and the logic behind the steps involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to clarify the logic behind the induction step, questioning how certain expressions are used in the proof. There is a focus on the relationship between terms in the sequence and the implications of the assumptions made.

Discussion Status

The discussion is ongoing, with participants providing insights and attempting to clarify the reasoning behind the induction steps. Some have offered partial explanations, while others are still grappling with the connections between the expressions involved.

Contextual Notes

There are references to specific expressions and steps in the proof that may not be fully articulated, indicating potential gaps in information or understanding. Participants are also considering the implications of the assumptions made in the proof process.

transgalactic
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i can't understand this step in this induction

http://img383.imageshack.us/img383/5677/99884212ia5.gif
 
Last edited by a moderator:
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Because if an + L - e < an+1,

then an + 2(L - e) < an+1 + L - e

but an+1 + L - e < an+2

so an + 2(L - e) < an+1 + L - e < an+2 :smile:

Now try it for the other half, and write it out properly as an induction proof. :wink:
 
in the total case of K
we are given some expression
and we presume that its true
so to prove the K+1 case

from where did they use the left side development
it seems that the are using the given expression itself to proove it
?
http://img149.imageshack.us/img149/6359/10189365rk3.gif
 
Last edited by a moderator:
this is the expanded proove
http://img220.imageshack.us/img220/1912/13164747xs4.gif
 
Last edited by a moderator:

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