Proof Error: Missing Link at n^4 Term

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Homework Help Overview

The discussion revolves around a proof by induction concerning a polynomial expression involving products of consecutive integers and their equivalence to a specific polynomial form. The original poster expresses concern about a potential error in the proof, particularly at the n^4 term, despite empirical validation for values of n up to 134.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants question the clarity of the original proof and the specific claims made, particularly regarding the missing link at the n^4 term. There are attempts to clarify the expression being proven and to identify any inconsistencies in the formulation.

Discussion Status

The discussion is ongoing, with participants seeking to understand the original poster's intent and the validity of the proof. Some guidance has been offered regarding the need for clearer definitions and the structure of the proof, but no consensus has been reached on the correctness of the proof itself.

Contextual Notes

There is a noted lack of clarity regarding the original statement of the proof, and some participants express confusion about the terms involved. The original poster indicates that the proof cannot be verified, suggesting potential constraints in the information provided.

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What is wrong with this proof? There seems to be a missing link at the n^4 term, even though values of n up to 134 are true!

http://www.geocities.com/jake_lloyd007/ind.jpg
 
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without seeing it all souldn't the answers to each line read as follows:

n+6n+11n+6n

n+10n+35n+50n+24n

n+11n+41n+61n+30n (if you add the two lines above together)
 
1. You haven't told us what you are trying to prove!

2. What you posted makes no sense! In the last line, there appears to be no n on the left side, yet the right side depends on n.
 
I am trying to preform a proof by induction that for any positive number n,

1 x 2 x 3 x 4 + 2 x 3 x 4 x 5 + ...+ n (n+1)(n+2)(n+3)(n+4)

= n^4 + 6n^3 + 11n^2 + 6n

So in the image just consider the k as n.

It's a polynomial with a pretty long expansion, but I have checked and rechecked and if there is an error, I can't find one. Yet it can't be proven?
 

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