- #1
ChelseaL
- 22
- 0
Deduce that
n
Sigma (2r)^3 = 2n^2 (n+1)^2
r=1I'm not exactly sure how to start.
n
Sigma (2r)^3 = 2n^2 (n+1)^2
r=1I'm not exactly sure how to start.
ChelseaL said:Deduce that
n
Sigma (2r)^3 = 2n^2 (n+1)^2
r=1I'm not exactly sure how to start.
ChelseaL said:The result of my previous thread was 1.
ChelseaL said:Oh right sorry, I got locked out of my previous account. The part with the k + 1 case?
ChelseaL said:1
sigma r^3 = 1^2(1+1)^2/4?
r=1
ChelseaL said:Deduce that
n
Sigma (2r)^3 = 2n^2 (n+1)^2
r=1
Sigma is a symbol that represents a mathematical sum or series. In this equation, it represents the sum of the first n cubes.
This equation was deduced using mathematical manipulation and simplification. The goal was to find a relationship between the sum of cubes and the square of a number (n+1).
2r represents the number of terms in the sum of cubes, while 2n^2 represents the square of the number of terms in the sum of squares. These terms are important in balancing out the equation and making it true.
Setting r to 1 simplifies the equation and makes it easier to understand and manipulate. It also helps to establish the relationship between the sum of cubes and the square of a number.
Yes, this equation can be applied to any positive integer values of n and r. However, it is most commonly used when n and r are set to 1.