Proving the Sum of an Arithmetic Series Formula

The Organic Chemistry Tutor

A focused mathematics tutorial that explains the difference between arithmetic sequences and series, demonstrates how to calculate the partial sum of a series, and provides a step-by-step algebraic proof for the arithmetic series sum formula. The video begins by distinguishing between a sequence (a list of numbers) and a series (the sum of those numbers) using a specific numerical example (5, 8, 11, 14, 17). The core of the video explores the derivation of the formula Sn = n/2 * (a1 + an). The instructor uses the "Gaussian method" of writing the series sum forwards and backwards, then adding the two equations together. This visual algebraic demonstration highlights how the common differences cancel out, leaving a clean result that proves why the formula works. This resource is highly valuable for high school Algebra II or Pre-Calculus classrooms. It moves beyond rote memorization by teaching the "why" behind the math. Teachers can use this to introduce the concept of formal proofs or to help students visualize the symmetry inherent in arithmetic progressions.