questionposter Posted April 18, 2012 Share Posted April 18, 2012 (edited) I'm trying to come up with a general formula to describe irrational numbers, by using the general summation of (1/n) , like an infinite summation of (1/3) = .33333333333 = 1/3, which isn't irrational, but I suspect irrational numbers can be decribed by some sort of summation that modulates with a base 10 or possibly a base = to some arithmetic form of n as to have a different modulus every time and thus never repeat. Though, every time I've ever thought of some cool mathematical thing, it terms out some dead scientist thought of it 100 years ago or more, so I'm just wondering if this has already been done. Edited April 18, 2012 by questionposter Link to comment Share on other sites More sharing options...

khaled Posted May 6, 2012 Share Posted May 6, 2012 (edited) I'm trying to come up with a general formula to describe irrational numbers, by using the general summation of (1/n) , like an infinite summation of (1/3) = .33333333333 = 1/3, which isn't irrational, but I suspect irrational numbers can be decribed by some sort of summation that modulates with a base 10 or possibly a base = to some arithmetic form of n as to have a different modulus every time and thus never repeat. Though, every time I've ever thought of some cool mathematical thing, it terms out some dead scientist thought of it 100 years ago or more, so I'm just wondering if this has already been done. I think you're talking about this, which looks ordinary: [math].333333 \approx \frac{1}{3} = .33333... = .\ddot{3}[/math] [math].\ddot{k} = .k + .0k + .00k + ... = \sum_{i=-1}^{-\infty}{{k}^{i}}[/math] Edited May 6, 2012 by khaled Link to comment Share on other sites More sharing options...

imatfaal Posted May 7, 2012 Share Posted May 7, 2012 [math] \sum_{i=-1}^{-\infty}{{k}^{i}} = \frac{1}{k}+\frac{1}{k^2}+\frac{1}{k^3}... [/math] thats not what you wanted. Take k=2 for instance - the sum of hte infinite series would be 1; basically you have defined a geometric series with a = 1/k and r as 1/k what would be correct would be the sum of the series [math] \sum_{i=-1}^{-\infty}{{k}*10^{i}} = \frac{k}{10}+\frac{k}{100}+\frac{k}{1000}... [/math] 1 Link to comment Share on other sites More sharing options...

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