# Exponential bound for Euler's zeta function?

## Main Question or Discussion Point

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?

## Answers and Replies

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

Gib Z,

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

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