Question: Determine if the series converges or diverges using the Alternating Series Test. If the series converges, determine if it converges conditionally or absolutely.

1. \(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}-\frac{1}{\sqrt{5}}+\frac{1}{\sqrt{6}}-\ldots\)
2. \(\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{\ln (n+4)}\)
3. \(\sum_{n=1}^{\infty}(-1)^{n-1} \frac{\ln n}{n}\)
4. \(\sum_{n=1}^{\infty}(-1)^{n} \cos \left(\frac{\pi}{n}\right)\)

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