Date: Oct 26, 1999 1:13 PM
Author: Kresimir Kumericki
Subject: Flies, trains, and series summation

[sci.physics.research removed]

In sci.physics Chris Hillman <hillman@math.washington.edu> wrote:

> On 22 Oct 1999, Phillip Helbig wrote:

>> The problem being: Two trains are 60 miles apart and approaching each

>> other at 30 miles per hour. There is a fly flying between the

>> cowcatchers of each train, at 60 miles per hour, back and forth, turning

>> around immediately. What is the total distance covered by the fly

> The problem you mention certainly strikes me as much too simple to have

> the ring of truth, since anyone could sum -that- series in their head in a

> few seconds!

Then, "ian" <walkersystems@one.net.au> wrote:

> why sum a series?

> it takes the trains 1 hour to hit, the fly travels at 60 m/hr so the fly

> flies 60 miles...

When I heard about this puzzle long time ago I got the idea

that perhaps this way you can sum some complicated series using

the following procedure:

Construct (complicated) trains-fly path such that the fly, flying to

and fro, travels distances equal to the terms of your series.

Than the distance traveled by train(s) equals the sum of the series.

Now, I was too lazy (and mathematically ignorant) to investigate

into this idea but I'd love to hear if this wouldn't work and why (too

trivial probably).

--

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Kresimir Kumericki kkumer@phy.hr http://www.phy.hr/~kkumer/

Theoretical Physics Department, University of Zagreb, Croatia

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