Asymptotics of Abs( Sum of sequence of rand var)



I am interested in the asymptotics of the absolute value of the (partial) sum of a sequence of random variables
Define X1...Xn iid with all moments finite
Denote Sn= X1+...+Xn
Show that Abs(Sn) = BigO (n^{0.5+epsilon})

All I know is that the proof uses the kth moment of Sn, E(Sn^k)
.



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