- #1

- 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]