Question

Which expression gives the sum of the first n odd natural numbers \[1 + 3 + \cdots + (2n-1)\]?

Options

• \[n^2\]

• \[(n-1)^2\]

• \[n(n+1)\]

• \[\frac{n(n+1)}{2}\]

Answer 1

The sum of the first n odd natural numbers is \[1 + 3 + \cdots + (2n-1) = n^2.\] For example, \[1 + 3 + 5 = 3^2 = 9.\]