Question

Which expression gives the sum of the first n even natural numbers \[2 + 4 + \cdots + 2n\]?

Options

• \[n^2\]

• \[\frac{2n(2n+1)}{2}\]

• \[n(n+1)\]

• \[\frac{n(n+1)}{2}\]

Answer 1

The sum of the first n even natural numbers is \[2 + 4 + \cdots + 2n = n(n+1).\] Note that \[\frac{2n(2n+1)}{2}\] is the sum of the first 2n natural numbers, not of the first n even numbers.