Does the infinite series $\sum_{t=1}^\infty t^2 e^{-\sqrt{L\ln t}}$ converge for any value of the constant L?
Absolute convergence of $\sum_{t=1}^\infty t^2 e^{-\sqrt{L\ln t}}$
2
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sequences-and-series
convergence-divergence
1 Answers
5
Hint: If $t$ is large enough, $\sqrt{L\ln t}\lt \ln t$. It follows that $e^{-\sqrt{L\ln t}} \gt \dots$.