Let $\displaystyle X_{1},...,X_{n}$ be independent random variables, that
$\displaystyle P(X_{i}=1)=1/i=1-P(X_{i}=0)$ and $\displaystyle K_{n}=X_{1}+...+x_{n}$
Show that $\displaystyle K_{n}/log(n) to1 $ with probability
Decide if $\displaystyle K_{n}/log(n) to 1 $ almost sure
Hint $\displaystyle \frac{sum_{k=1}^{n}1/k}{log(n)}\arrow $

Thx for any help