# Bose function convergence

## Homework Statement

How can I show that this series is convergent for z=1 and z<1 and divergent for z>1

$$\sum _{p=1}^{\infty }\dfrac {z^{p}} {p^{3/2}}$$

## Homework Equations

http://tutorial.math.lamar.edu/Classes/CalcII/RatioTest.aspx

## The Attempt at a Solution

Using the ratio test I've found:

$$\lim _{p\rightarrow \infty }\sum _{p=1}^{\infty }\dfrac {z^{p}} {\left( p+1\right) ^{3/2}}$$
[/B]

$$\sum_{p = 1}^{\infty} a_{p},$$
$$\lim_{p \to \infty} \frac{a_{p+1}}{a_{p}}.$$