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        riddles >> putnam exam (pure math) >> Sum of alternating primes
        
(Message started by: JocK on Aug 4^th, 2007, 9:44am)

Title: Sum of alternating primes
Post by JocK on Aug 4^th, 2007, 9:44am

can you regularise 2 - 3 + 5 - 7 + 11 - 13 + 17 - 19 + 23 - 29 + 31 - 37 + ... ???

Title: Re: Sum of alternating primes
Post by towr on Aug 4^th, 2007, 11:27am

What is 'regularising'?

Title: Re: Sum of alternating primes
Post by Eigenray on Aug 4^th, 2007, 9:52pm

For example,

1 + 2 + 3 + 4 + ... "=" [hide]-1/12[/hide],

and

1*2*3*4*... "=" [hide]\sqrt{2\pi}[/hide],

by a naive interpretation of [hide]zeta(-1) and zeta'(0)[/hide], respectively.

Title: Re: Sum of alternating primes
Post by JocK on Aug 5^th, 2007, 2:03am

Some more background can be found in:

http://en.wikipedia.org/wiki/Divergent_series