Does (X_{n})_{n_{\geq 1}} converge almost surely to 0?

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yavanna
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Does [tex](X_{n})_{n_{\geq 1}}[/tex], [tex]X_{n}=\frac{n}{ln(n)}Y_{n}[/tex], where [tex]Y_{n} \sim Exp(n)[/tex] converge a.s. to 0?
 
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