Determine whether the following series converge or diverge. Answer "Converges" or "Diverges."

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? Converges Diverges 1. $\displaystyle \sum_{n=1}^{\infty} n\left(\frac{5}{3}\right)^n$

? Converges Diverges 2. $\displaystyle \sum_{n=1}^{\infty}\frac{100^{n}}{n!}$

? Converges Diverges 3. $\displaystyle \sum_{n=1}^{\infty}\frac{\sin 6 n}{6^n}$

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Note: You only have two attempts at this problem.

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