# Corollary of Kolmogorov zero-one law [duplicate]

Here is another corollary of the theorem: Kolmogorov zero-one law given in my textbook (Probability path). How can I apply the said theorem given that if $X_n$ are independent random variables, $[\sum_nX_n \mbox{ converges}]$ has probability 0 or 1. thanks :-)
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Hint: show that this event is in the tail $\sigma$-field.