121616949-math.247 - and more terms the sum gets closer and...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
10 Sequences and Series Consider the following sum: 1 2 + 1 4 + 1 8 + 1 16 + · · · + 1 2 i + · · · The dots at the end indicate that the sum goes on forever. Does this make sense? Can we assign a numerical value to an infinite sum? While at first it may seem difficult or impossible, we have certainly done something similar when we talked about one quantity getting “closer and closer” to a fixed quantity. Here we could ask whether, as we add more
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: and more terms, the sum gets closer and closer to some fixed value. That is, look at 1 2 = 1 2 3 4 = 1 2 + 1 4 7 8 = 1 2 + 1 4 + 1 8 15 16 = 1 2 + 1 4 + 1 8 + 1 16 and so on, and ask whether these values have a limit. It seems pretty clear that they do, namely 1. In fact, as we will see, it’s not hard to show that 1 2 + 1 4 + 1 8 + 1 16 + ··· + 1 2 i = 2 i-1 2 i = 1-1 2 i 233...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern