Proof Without Words – Part 6

Algebra Level 4

The image above illustrates which of the following identities?

1 + 3 + 5 + \dots + (2n-1) = n^2

1^3 + 2^3 + 3^3 + \dots + n^3 = \frac{1}{4}\left[n(n+1)\right]^2

1^2 + 2^2 + 3^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6}

1^3 + 2^3 + 3^3 + \dots + n^3 = (1 + 2 + 3 + \dots + n)^2