Prove formula (e) of Theorem 3 using the following method published by Abu Bekr Mohammed ibn Alhusain Alkar-chi in about ad 1010. The figure shows a square ABCD in which sides AB and AD have been divided into segments of lengths 1, 2, 3, …, n. Thus the side of the square has length n(n + 1)/2 so the area is [n(n + 1)/2]2. But the area is also the sum of the areas of the n “gnomons” G1, G2, ..., Gn shown in the figure. Show that the area of Gi is i3 and conclude that formula (e) is true.
Trending nowThis is a popular solution!
Chapter E Solutions
Single Variable Calculus: Early Transcendentals
Additional Math Textbook Solutions
Precalculus: A Unit Circle Approach (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals, Single Variable (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus
Finite Mathematics and Calculus with Applications (10th Edition)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage