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

  • MHB
  • Thread starter Harry2
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In summary, the conversation is about showing that 3r(r+1) is equal to r(r+1)(r+2) - r(r-1)(r+1) and finding the total sum of r(r+1). The suggestion is to try factoring the right hand side and noticing that each 'r' term on the right is 1 less than an 'r' term on the left.
  • #1
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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  • #2
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.
 
  • #3
To show:

\(\displaystyle 3r(r+1)=r(r+1)(r+2) - r(r-1)(r+1)\)

try factoring the RHS. :)
 
  • #4
MarkFL said:
To show:

\(\displaystyle 3r(r+1)=r(r+1)(r+2) - r(r-1)(r+1)\)

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!
 

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

What is the equation "Solving 3r(r+1)=r(r+1)(r+2)-r(r-1)(r+1) and Finding r(r+1) Sum" trying to solve?

The equation is trying to solve for the value of r that makes the left side of the equation equal to the right side.

How do I solve the equation "Solving 3r(r+1)=r(r+1)(r+2)-r(r-1)(r+1) and Finding r(r+1) Sum"?

To solve this equation, you can use the distributive property to simplify the right side of the equation. Then, combine like terms on both sides and solve for r.

Why is it important to find the value of r(r+1) in this equation?

The value of r(r+1) is important because it represents the sum of two consecutive numbers, which is often used in mathematical equations and can provide important information about a set of numbers.

Are there any specific steps or methods to follow when solving this equation?

Yes, there are several steps you can follow to solve this equation. First, use the distributive property to simplify the right side. Then, combine like terms and solve for r. You can also check your solution by plugging it back into the original equation.

Can this equation be solved without using algebraic methods?

No, this equation cannot be solved without using algebraic methods. However, you can use a calculator to help you simplify the equation and solve for r.

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