anemone
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For $n=1,2,...,$ set $$S_n=\sum_{k=0}^{3n} {3n\choose k}$$ and $$T_n=\sum_{k=0}^{n} {3n\choose 3k}$$.
Prove that $|S_n-3T_n|=2$.
Prove that $|S_n-3T_n|=2$.