Algebra problem ordinary numbers

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Homework Help Overview

The discussion revolves around simplifying a factorial expression involving ordinary numbers, specifically transitioning from the expression (k+1)!(k+2) - 1 to (k+2)! - 1. Participants are exploring the properties of factorials and their relationships.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to manipulate the factorial expressions step by step and are questioning the validity of the transformations. There is a focus on understanding how (k + 2)! relates to (k + 2)(k + 1)!. Some participants express confusion about the factorial definitions and seek clarification on the steps involved.

Discussion Status

The discussion is ongoing, with participants providing their interpretations and questioning each other's reasoning. Some have offered insights into the factorial relationship, while others are still grappling with the concepts and seeking further explanation.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for discussion. There is an emphasis on step-by-step reasoning and clarification of definitions related to factorials.

synkk
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http://www.wolframalpha.com/input/?i=(k+1)!(k+2)+-1

Could anyone explain how you get from (k+1)!(k+2) - 1 to (k+2)! - 1

step by step please, here is my attempts:

(k+1)k!(k+2) - 1
(k+1)(k+2)k! - 1
(k+1)(k+2)! -1
no idea where to go from here
 
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synkk said:
http://www.wolframalpha.com/input/?i=(k+1)!(k+2)+-1

Could anyone explain how you get from (k+1)!(k+2) - 1 to (k+2)! - 1
This is very straightforward. (k + 2)! = (k + 2)*(k + 1)!
synkk said:
step by step please, here is my attempts:

(k+1)k!(k+2) - 1
(k+1)(k+2)k! - 1
(k+1)(k+2)! -1
no idea where to go from here
 
Mark44 said:
This is very straightforward. (k + 2)! = (k + 2)*(k + 1)!

how? isn't (k+2)*(k+1)k!? how is that (k+2)!?
 
synkk said:
how? isn't (k+2)*(k+1)k!?
Isn't (k+2)*(k+1)k! what?
synkk said:
how is that (k+2)!?

(k + 2)! = (k + 2)*(k + 1)! = (k + 2) * (k + 1) * k!

Let's look at ordinary numbers.

8! = 8 * 7! = 8 * 7 * 6!
= 8 * 7 * (6 * 5 * 4 * 3 * 2 * 1)
= 56 * 720 = 40320
 

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