Any budding mathematicians? Any flaws in this ?
vitaminl.tv/video/2240
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Good fun. The problem I always have with those kind of things is that as soon as they say "add up all the numbers to infinity" my brain says whoa, stop, can't be done, it's a house of sand. After that it's amusing but seems unreal.
But they say it yields actual results that are usable in the real world. That's the more interesting bit and wasn't explained there.
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I looked at asymptotic theory, which, rummaging in the Wiki information, led on to description of Cesàros summation, which is where the first sequence (with the result of 1/2) derives. My brain hurts.
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Beyond my 'O' level maths. I had enough problems understanding the square root of minus one!
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In the engineering maths I do, when there's an answer which drops out as an infinite sum, the sum tends to be convergent - usually, rapidly so - phrased another way, the successive contributing terms to the sum tend towards zero faster than they contribute to the sum (with apologies to mathematcians who would prefer more rigour in that definition!)
I admit, while the square root of minus one is massively useful to me, and I would be stuck without it, these sums which don't converge seem rather magical to me, and I've never had a need to use them. Interesting though.
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Stranger than you think? - Crankcase
