# law of large numbers

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• Feb 12th 2011, 12:39 PM
slavert
law of large numbers
Let $X_{1},...,X_{n}$ be independent random variables, that
$P(X_{i}=1)=1/i=1-P(X_{i}=0)$ and $K_{n}=X_{1}+...+x_{n}$
Show that $K_{n}/log(n) to1$ with probability
Decide if $K_{n}/log(n) to 1$ almost sure
Hint $\frac{sum_{k=1}^{n}1/k}{log(n)}\arrow$

Thx for any help