11 points to the person who can satisfactorily explain my conundrum

Let x = 1 + 1/2 + 1/4 + 1/6 ...

x-1 = 1/2 + 1/4 + 1/6 ...

2(x-1) = 1 + 1/2 + 1/3 + 1/4 ...

We can pull x out of the right side to get,

2(x-1) = (1/3 + 1/5 + 1/7 + ...) + x

x-2 = 1/3 + 1/5 + 1/7 + ...

x = 2 + 1/3 + 1/5 + 1/7 + ...

We substitute for x and get,

1 + 1/2 + 1/4 + 1/6 ... = 2 + 1/3 + 1/5 + 1/7 + ...

1/2 + 1/4 + 1/6 + 1/8 ... = 1 + 1/3 + 1/5 + 1/7 + ...

But, how can this be?  Every term on the right is greater than a corresponding term on the left. 1 > 1/2, 1/3 > 1/4 etc, etc, etc.)

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~ by wcuk on August 6, 2008.

8 Responses to “11 points to the person who can satisfactorily explain my conundrum”

  1. x – 2 = 1/3 + 1/5 + 1/7 + …
    x – 1 = 1 + 1/3 + 1/5 + 1/7 + …

    so the right side of the last line is = x – 1

    x = 1 + 1/2 + 1/4 + 1/6 + …
    x – 1 = 1/2 + 1/4 + 1/6 + …

    so the left side of the last line is x – 1

    x – 1 = x – 1

    bitches

  2. withdrawn. shit.

  3. i must really want these stupid points.

    1/2 + 1/4 + 1/6 + … is a divergent series. solved ad infinitum, it yields a value of infinity.

    1 + 1/3 + 1/5 + 1/7 … is also a divergent series. it also yields a value of infinity.

    the two values approach infinity. while they approach it at different rates, they still are equal in terms of limit.

    darn you, sir. darn you to heck.

  4. I am going to call Don’s answer 70% correct. That leaves 1 – 7/11 = 3.63 points still up for grabs to the person who can, as they say in Mortal Kombat, FINISH HIM.

  5. Yes, Don is on the right track. But if he’s 70% correct, why doesn’t he get 70% of the available points? (0.7 * 11 = 7.7)

    Anyhow, you went all wrong at step 2. As Don said, x = 1 + 1/2 + 1/4 . . . is divergent . . . to INF. So in step 2, you are subtracting 1 from INF. 1 – INF is undefined (a.k.a. INF).

  6. Winner winner, chicken dinner.

    In addition, I am subtracting 4 points from myself for my incompetence in basic arithmetic.

  7. Soooo . . . looking at the leaderboard . . . Don got 7.37 points? What, is this like Who’s Line Is It Anyway where the points don’t matter?

  8. BITE YOUR TONGUE. THE POINTS. MEAN. EVERYTHING.

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