Proof Without Words: Sums of Powers of Natural numbers

TL;DR

This paper provides visual, non-verbal proofs for the sum formulas of natural number powers for k=1, 2, and 3, enhancing understanding through geometric representations.

Contribution

It introduces a proof without words for the sum formulas of natural number powers specifically for k=1, 2, and 3, which is a novel visual approach.

Findings

Visual proofs for sum formulas of powers 1, 2, and 3

Enhanced understanding of sum formulas through geometric representations

Simplified non-verbal proofs for educational purposes

Abstract

The aim of this paper is to prove wordlessly the sum formula of $1^{k}+2^{k}+\ldots +n^{k}$, $k\in\{1,2,3\}$.