- #1
bob1182006
- 492
- 1
Homework Statement
Show:
[tex]\sum_{i=1}^n (x_i - \overline{x}) = 0[/tex]
Homework Equations
Sigma notation
The Attempt at a Solution
[tex]\sum_{i=1}^n x_i - \sum_{i=1}^n \overline{x} = \sum_{i=1}^n x_i - \frac{1}{n}\sum_{i=1}^n \sum_{i=1}^n x_i = 0[/tex]
[tex]\sum_{i=1}^n x_i = \frac{1}{n}\sum_{i=1}^n \sum_{i=1}^n x_i [/tex]
By Inspection I know i need to show that:
[tex]\sum_{i=1}^n \frac{1}{n}=1[/tex]
Since the LHS has no [itex]x_i[/itex] how can i show that the sum will result in n/n =1?
Is it just:
[tex]\sum_{i=1}^n 1 = n?[/tex]