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