\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For \(\alpha \in \{1/2, 1, 3/2, 2, 3\}\), determine the nature of \(\sum_{n \ge 1} 1/n^\alpha\) by direct application of the Riemann Theorem.
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