The mystery of 0.577 - Numberphile
The harmonic series and the elusive Euler–Mascheroni constant. More links & stuff in full description below ↓↓↓ Featuring Dr Tony Padilla. Audible: http://www.audible.com/numberphile...
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I wanna start in a nice, familiar, comfortable place, Brady. Which is this series: 1.. +2 .. +3 ..+4 Oh no! Oh no! Alright, all the way up to infinity. You remember what the answer to that was? Yeah. Yeah, what was it? it's a, uh, divergent sum. Yeah, it's -1/12, isn't it? Which is totally uncontroversial. that's that's not weird at all. so I'm not actually going to talk about that series but I want to talk about something thats related to that series so I want to consider what happens when we take the reciprocal of all these numbers and take the sum of those so we take 1 + a half + a third + a quarter + a fifth. what would we get if we added all these numbers together you can look at this and you might think even though someone g...
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I wanna start in a nice, familiar, comfortable place, Brady. Which is this series: 1.. +2 .. +3 ..+4 Oh no! Oh no! Alright, all the way up to infinity. You remember what the answer to that was? Yeah. Yeah, what was it? it's a, uh, divergent sum. Yeah, it's -1/12, isn't it? Which is totally uncontroversial. that's that's not weird at all. so I'm not actually going to talk about that series but I want to talk about something thats related to that series so I want to consider what happens when we take the reciprocal of all these numbers and take the sum of those so we take 1 + a half + a third + a quarter + a fifth. what would we get if we added all these numbers together you can look at this and you might think even though someone g...
