- #1
erbilsilik
- 20
- 2
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:
$$\lim _{p\rightarrow \infty }\sum _{p=1}^{\infty }\dfrac {z^{p}} {\left( p+1\right) ^{3/2}}$$
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