1. Use the (Direct) Comparison Test to determine if each of the following series is convergent or divergent.
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(a) \(\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2 + 3n + 5}\) View Video Solution |
(c) \(\displaystyle \sum_{n=1}^{\infty} \frac{2^n}{3^n + 1}\) View Video Solution |
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(b) \(\displaystyle \sum_{n=1}^{\infty} \frac{n^2}{n^3 - 2}\) View Video Solution |
(d) \(\displaystyle \sum_{n=1}^{\infty} \frac{\cos^2 n}{n^3}\) View Video Solution |
2. Use the Limit Comparison Test to determine if each of the following series is convergent or divergent.
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(a) \(\displaystyle \sum_{n=1}^{\infty} \frac{1}{3n + 5}\)
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(b) \(\displaystyle \sum_{n=1}^{\infty} \frac{5n^4 + 2 \cdot 3^n - 1}{2n^4 + 4^n + 2}\)
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(c) \(\displaystyle \sum_{n=1}^{\infty} \frac{n-1}{3n \sqrt{n}}\)
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(d) \(\displaystyle \sum_{n=1}^{\infty} \frac{2n^2 - 3n + 5}{3n^4 + 5n^2 + 4n - 3}\)
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(e) \(\displaystyle \sum_{n=5}^{\infty} \frac{n+6}{(n+3)^{5}}\)
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(f) \(\displaystyle \sum_{n=1}^{\infty} \frac{7n + 3^{n}}{2n + 5^{n}}\)
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