# Does this infinite series converge

Does the infinite series $\sum_{t=1}^\infty t^2 e^{-\sqrt{L\ln t}}$ converge for any value of the constant L?

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Hint: If $t$ is large enough, $\sqrt{L\ln t}\lt \ln t$. It follows that $e^{-\sqrt{L\ln t}} \gt \dots$.