Sum of Consecutive Odd Numbers

Sum of Consecutive Odd Numbers

## Formula

The sum of the first $$n$$ odd numbers is:

$$1+3+\cdots+(2n-1)=n^2$$

The sum of odd numbers from $(2m-1)$ to $(2n-1)$ is:

$$\sum_{k=m}^{n}(2k-1)=n^2-(m-1)^2$$

## Usage

- Used to calculate sums over selected ranges of consecutive odd numbers.