Jan 18, 2025
Sum of squares and cubes, using difference calculus.
[Click here for a PDF version of this post] Motivation. I showed Karl Gauss’s trick for summing a \( 1, 2, \cdots, n \) sequence. Add it up twice, reversing the sum and adding by columns \begin{equation}\label{eqn:sumOfSquares:21} \begin{array}{c|c|c|c|c} 1 & 2 & \cdots & n-1 & n \\ n & n-1 & \cdots & 2 & 1 \end{array} \end{equation} We get \( n + 1 \), \( n \) times,…