Let ##X_i## are i.i.d. and take -1 and +1 with probability 1/2 each. How to prove ##\lim_{n\rightarrow\infty}{\sum_{i=1}^{n}{X_i} }##does not exsits (even infinite limit) almost surely.(adsbygoogle = window.adsbygoogle || []).push({});

My work:

I use cauchy sequence to prove it does not converge to a real number.

But I do not how to prove it does not converge to infinity. Can some one give hints?

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# The limit of random variable is not defined

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