Exponential bound for Euler's zeta function?

[Loren Booda]

Let Euler's zeta function be given by

$$\sum_{n=1}^{\infty}1/n^s$$

Is there an exponent L which limits the finiteness of

$$(\sum_{n=1}^{\infty}1/n^s)^L$$

for the case where s=1?

 

[Gib Z]

When s=1, that series diverges, so there is no value of L that would make it finite.

 

[Loren Booda]

Gib Z,

The ineffectiveness of an exponential on a diverging sequence should have been obvious to me.

 

[Gib Z]

Don't worry, we all have brain farts once in a while =]