On 27/07/2015 01:56 PM, scott wrote:
>>> s= 1+2+3+4+5+6+...
>>>
>>
>> Nah, s does *NOT* converge, insisting that s exists get you what you
>> deserve: bullshit (unless you are interested in classification of
>> divergent series).
>
> It does seem absurd, that the result comes out negative and less than
> even the smallest term in the sequence. Saying that though the steps
> seem logical enough (from a practical point of view rather than a
> mathematical point of view) to come to the answer of -1/12.

It seems the idea is to replace Sum[n] with Sum[n^-s], which is the 
definition of the Riemann zeta function. The new series doesn't converge 
for the value of interest, but by analytic continuation you can figure 
out a suitable value that makes it "fit in with" the other values.

It's a little like... what is b^0.5? How do you multiply something by 
itself half a time? That doesn't even make *sense*! But if you 
extrapolate from the values that *do* make sense... you come to a simple 
and even rather useful result.

> But according to the wikipedia page below the -1/12 thing does have some
> practical uses? I couldn't find any actual information about those
> practical uses though.

Well, as "practical" as the Riemann zeta function I guess...

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