Mathematics Made Simple : Sixth Edition by Thomas Cusick

Looking to improve your math skills? Look no further! Whether you need a quick refresher or a detailed overview, Mathematics Made Simple is the ultimate resource for mastering the basics. This comprehensive book offers clear, concise lessons that make math enjoyable to learn.

Mathematics Made Simple covers a wide range of topics, including fractions, decimals, percents, algebra, linear equations, graphs, probability, geometry, and trigonometry. Each concept is explained step by step, with easy-to-follow solutions provided for every problem.

To track your progress, this book includes multiple choice tests that allow you to assess your understanding. Additionally, there is a comprehensive final test that helps pinpoint your strengths and areas that need improvement.

In addition to the main content, Mathematics Made Simple also includes glossaries of mathematical terms and sidebars that demonstrate real-life applications of these principles.

Say goodbye to lengthy explanations and difficult computations. With Mathematics Made Simple, you can overcome math anxiety and develop a solid foundation in math.

Infinite Series and a Clever Picture: Exploring the Sum of Fractional Numbers

What is the sum of one half plus one fourth plus one eighth, and so on indefinitely? At first glance, it may seem like the sum would be infinite, but upon closer examination, we can discover that the total is actually finite. We don’t need advanced calculus to solve this problem; all we need is a clever visual representation.

Let’s imagine a square where each side represents one unit. To start, we shade in an area that accounts for one half of the square. Next, we shade in another area that represents one fourth of the square. Then, we add yet another shaded area to represent one eighth of the square. As we continue this process, we will keep adding smaller and smaller shaded areas to our square.

The next step would be shading in an area representing one sixteenth, followed by one thirty-second, one sixty-fourth, and so on. As we keep going, the shaded areas become increasingly minuscule.

Eventually, what emerges is a square with a total shaded area of one. This tells us that the sum of one half plus one fourth plus one eighth, and so on indefinitely, equals one.

So, to answer the initial question, the sum is not infinite. Instead, it converges to a finite value of one. This clever visual representation helps us comprehend that the numbers may become smaller, but their sum eventually settles at a definite answer.