Problems 003

By -
What is 1/1 + 2/2 + 3/4 + 4/8 + 5/16 + 6/32 + ...?

Comments

  1. Jared9:53 AM

    We can write this:
    1/1 + 1/2+1/2 + 1/4+1/4+1/4 + 1/8+1/8+1/8+1/8 + ...
    It is absolutely convergent, so we can rearrange it:
    (1/1+1/2+1/4+...)+(1/2+1/4+1/8+...)+(1/4+1/8+1/16...)+....
    =2+1+1/2+1/4+1/8+...
    =4

    ReplyDelete
  2. Wabulon7:18 PM

    Yup. I included 003 for the sake of 004.

    ReplyDelete

Post a Comment

Popular posts from this blog

Libertarians, My Libertarians!

By -
Cruel to be kind means that I love you . Because, while I think you are mistaken, your hearts are in the right place -- yes, even you, Silas --  unlike some people . This Breitbart fellow (discussed in the link above), by all appearances, deliberately doctored a video of Shirley Sherrod to make her remarks appear virulently racist, when they had, in fact, the opposite import. I heard that at a recent Austrian conference, some folks were talking about "Callahan's conservative turn." While that description is not entirely inaccurate, I must say that a lot of these people who today call themselves conservative give me the heebie-jeebies.
Read more

"Pre-Galilean" Foolishness

By -
 I am currently reading The Master and His Emissary , which appears to be an excellent book. ("Appears" because I don't know the neuroscience literature well enough to say for sure, yet.) But then on page 186 I find: "Asking cognition, however, to give a perspective on the relationship between cognition and affect is like asking astronomer in the pre-Galilean geocentric world, whether, in his opinion, the sun moves round the earth of the earth around the sun. To ask a question alone would be enough to label one as mad." OK, this is garbage. First of all, it should be pre-Copernican, not pre-Galilean. But much worse is that people have seriously been considering heliocentrism for many centuries before Copernicus. Aristarchus had proposed a heliocentric model in the 4th-century BC. It had generally been considered wrong, but not "mad." (And wrong for scientific reasons: Why, for instance, did we not observe stellar parallax?) And when Copernicus propose
Read more