Alternating series test, with derivative trick required to show the terms are decreasing.

Alternating Geometric Series This is a short, animated visual proof demonstrating the infinite alternating geometric series formula for any positive ratio r with r less than 1 and with positive first term a. This series is important for many results in calculus, discrete mathematics, and combinatorics. To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! For a slower, wide format version of this video (without words), see https://youtu.be/Qa0bOHYjnW0 Also, check out