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Let  $\left\{a_{n}\right\}$ be a sequence of real numbers. Which of the following is true?

1. If $\sum a_{n}$ converges, then so does $\sum a_{n}^{4}$
2. If $\sum |a_{n}|$ converges, then so does $\sum a_{n}^{2}$
3. If $\sum a_{n}$ diverges, then so does $\sum a_{n}^{3}$
4. If $\sum |a_{n}|$ diverges, then so does $\sum a_{n}^{2}$

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