Section 11.5: Alternating Series

Use the Alternating Series Test (AST) to determine if each of the following series is convergent. If the AST does not apply, use an appropriate test to conclude if the series converges or diverges.

1. (a) \(\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1} \frac{1}{n}\)
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2. (b) \(\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1} \frac{1}{\sqrt{n^{\pi}}}\)
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3. (c) \(\displaystyle \sum_{n=1}^{\infty} (-1)^{n} \frac{2n}{3n-1}\)
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4. (d) \(\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1} \frac{1}{4+n^2}\)
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5. (e) \(\displaystyle \sum_{n=1}^{\infty} (-1)^{n} n \, e^{-n}\)
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6. (f) \(\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1} \frac{n^{2}}{n^{2}+n+1}\)
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7. (g) \(\displaystyle \frac{1}{\ln 2} - \frac{1}{\ln 3} + \frac{1}{\ln 4} - \frac{1}{\ln 5} + \frac{1}{\ln 6} - \cdots\)
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