Solving 3r(r+1)=r(r+1)(r+2)-r(r-1)(r+1) and Finding r(r+1) Sum

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Discussion Overview

The discussion revolves around the equation 3r(r+1) = r(r+1)(r+2) - r(r-1)(r+1) and the subsequent task of finding the total sum of r(r+1). The focus is primarily on algebraic manipulation and verification of the equation.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance in demonstrating the equality of the two expressions.
  • Another participant suggests expanding the right-hand side of the equation as a potential method to show the equality.
  • A different participant proposes factoring the right-hand side as an alternative approach to verify the equation.
  • There is a mention of a concern regarding the order of operations in a "show that" question, indicating some uncertainty about the approach to take.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best method to demonstrate the equality, and multiple approaches are being discussed without resolution.

Contextual Notes

There are indications of missing assumptions regarding the methods of manipulation and the implications of the "show that" nature of the problem.

Harry2
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Hey,
Please may someone help me.
How can I show that 3r(r+1) is equal to r(r+1)(r+2) - r(r-1)(r+1) and then I would find the total sum of r(r+1).
Thanks in advance for any help.
 
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Have you tried expanding r(r+1)(r+2) - r(r-1)(r+1)?

To find the sum, notice that each 'r' term on the right is 1 less than an 'r' term on the left.
 
To show:

$$3r(r+1)=r(r+1)(r+2) - r(r-1)(r+1)$$

try factoring the RHS. :)
 
MarkFL said:
To show:

$$3r(r+1)=r(r+1)(r+2) - r(r-1)(r+1)$$

try factoring the RHS. :)

I just thought you couldn't use the right hand side first because it was a show that question. Thanks both of you!
 

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