Cool number stuff
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13-12-2011, 01:26 AM
Question RE: Cool number stuff
(13-12-2011 01:13 AM)cufflink Wrote:  Pi squared over 6! It's amazing to me how pi gets involved with things that have nothing to do with circles and diameters.

Pi is a schneaky beast, that's for sure.

Also how cool is it that if you *don't* square em and add em up, like this:
1 / 1 + 1 / 2 + ... + 1/n + ...

then it never converges to a number - just keeps on getting bigger and bigger and bigger, even though you're adding tinier and tinier amounts to it. If you keep doing that with that series (the harmonic series I think Tongue Can't remember name and lazy to google) you will eventually reach 100, 100 000 , 100 000 000 and in fact, any number. Might take you a while though Tongue
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13-12-2011, 02:19 AM
RE: Cool number stuff
(13-12-2011 01:26 AM)morondog Wrote:  
(13-12-2011 01:13 AM)cufflink Wrote:  Pi squared over 6! It's amazing to me how pi gets involved with things that have nothing to do with circles and diameters.

Pi is a schneaky beast, that's for sure.

Also how cool is it that if you *don't* square em and add em up, like this:
1 / 1 + 1 / 2 + ... + 1/n + ...

then it never converges to a number - just keeps on getting bigger and bigger and bigger, even though you're adding tinier and tinier amounts to it. If you keep doing that with that series (the harmonic series I think Tongue Can't remember name and lazy to google) you will eventually reach 100, 100 000 , 100 000 000 and in fact, any number. Might take you a while though Tongue

Yup. It's the harmonic series, all right. And it does diverge . . . but, as you said, very slowly. To get the sum to reach 100, you need approximately 1.509 X 10^43 terms!

Religious disputes are like arguments in a madhouse over which inmate really is Napoleon.
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13-12-2011, 02:32 AM
RE: Cool number stuff
(13-12-2011 02:19 AM)cufflink Wrote:  To get the sum to reach 100, you need approximately 1.509 X 10^43 terms!

So I think the general rule we have here is, if you want to count to 100, don't use the harmonic series Smile
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