- In a message dated 05/06/03 06:26:35 GMT Daylight Time, marku606@...

writes:

> It strains my brains that the sum could fall from infinite to finite

Why so?

> with (I presume) an infinitely small increment of the n exponent.

>

tan(theta) falls from infinite to finite for an infinitely small increment of

theta from pi/2...

Mike Oakes

[Non-text portions of this message have been removed] - '> It strains my brains that the sum could fall from infinite to finite
> with (I presume) an infinitely small increment of the n exponent.

Infinitely or finitely?

> '

Consider 1/e. As e->0 the expression has a value, at e=0 it is undefined.

This is basic continuity theory.

The behaviour of zeta(s) around s=1 is analysed at;

http://numbers.computation.free.fr/Constants/Miscellaneous/zeta.html

Jon Perry

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