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

  • Context: MHB 
  • Thread starter Thread starter Harry2
  • Start date Start date
  • Tags Tags
    Sum
Click For Summary
SUMMARY

The equation 3r(r+1) is proven to be equal to r(r+1)(r+2) - r(r-1)(r+1) through algebraic manipulation. By expanding the right-hand side and factoring, one can demonstrate the equality. Additionally, to find the total sum of r(r+1), it is essential to recognize that each 'r' term on the right is one less than the corresponding term on the left. This understanding aids in simplifying the expression effectively.

PREREQUISITES
  • Understanding of algebraic manipulation and factoring
  • Familiarity with polynomial expressions
  • Knowledge of summation concepts in mathematics
  • Ability to work with equations and inequalities
NEXT STEPS
  • Explore polynomial expansion techniques
  • Study factoring methods for quadratic expressions
  • Learn about summation formulas for polynomial sequences
  • Investigate the properties of algebraic identities
USEFUL FOR

Students, educators, and anyone interested in algebraic problem-solving, particularly those working with polynomial equations and summation concepts.

Harry2
Messages
5
Reaction score
0
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.
 
Physics news on Phys.org
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!
 

Similar threads

Graduate Solving a power series
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Function expansion in Cartesian and spherical tensors
  • · Replies 1 ·
Replies
1
Views
1K
High School How does this derivative work? And why the speed of light remains?
  • · Replies 7 ·
Replies
7
Views
426
MHB Proving Equation (1): Let r(t) be a Vector in $\mathbb{R^3}$
  • · Replies 2 ·
Replies
2
Views
1K
High School Having trouble deriving the volume of an elliptical ring toroid
  • · Replies 4 ·
Replies
4
Views
4K
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
  • · Replies 1 ·
Replies
1
Views
3K
MHB Are $\vec{r}$ and $\frac{d^2\vec{r}}{dt^2}$ Parallel When m+n=1?
  • · Replies 6 ·
Replies
6
Views
1K
MHB Revolving Volume of R on x=3 using Shell Method
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad What would a calculus author have to say on ##\int r^2dm##?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Calculate limits as distributions
  • · Replies 4 ·
Replies
4
Views
2K