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Topic: Sum of alternating primes (Read 835 times) 

JocK
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Sum of alternating primes
« on: Aug 4^{th}, 2007, 9:44am » 
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can you regularise 2  3 + 5  7 + 11  13 + 17  19 + 23  29 + 31  37 + ...


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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
x^{y}  y = x^{5}  y^{4}  y^{3} = 20; x>0, y>0.



Eigenray
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Re: Sum of alternating primes
« Reply #2 on: Aug 4^{th}, 2007, 9:52pm » 
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For example, 1 + 2 + 3 + 4 + ... "=" 1/12, and 1*2*3*4*... "=" \sqrt{2\pi}, by a naive interpretation of zeta(1) and zeta'(0), respectively.

« Last Edit: Aug 4^{th}, 2007, 9:59pm by Eigenray » 
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JocK
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Re: Sum of alternating primes
« Reply #3 on: Aug 5^{th}, 2007, 2:03am » 
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Some more background can be found in: http://en.wikipedia.org/wiki/Divergent_series


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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
x^{y}  y = x^{5}  y^{4}  y^{3} = 20; x>0, y>0.



