# Proving that a sequence of random variables satisfies Lindeberg's condition

I have a sequence of iid random variables $X_n$ with zero mean and constant variance $\sigma^2_n$. Let $S_n=\sum_{j=1}^{n}{(j-1)X_j}$. In order to prove asymptotic normality I need to prove first Lindeberg's condition.

Can anyone point me to the right direction?

Best regards,

Juan

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Can you write the Lindeberg's condition? – Davide Giraudo Dec 6 '11 at 19:49