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Convergence Tests Limit Comparison Test Worksheets

Series

Convergence Tests

Limit Comparison Test

1. convergence\:\sum_{n=1}^{\infty}\frac{n}{n^{2}+1}

1. convergence\:\sum_{n=1}^{\infty}\frac{n}{n^{2}+1}

2. convergence\:\sum_{n=1}^{\infty}\frac{2n-1}{n^{2}+n}

2. convergence\:\sum_{n=1}^{\infty}\frac{2n-1}{n^{2}+n}

3. convergence\:\sum_{n=1}^{\infty}\frac{n^{2}}{n^{3}+1}

3. convergence\:\sum_{n=1}^{\infty}\frac{n^{2}}{n^{3}+1}

4. convergence\:\sum_{n=1}^{\infty}\frac{1}{4n+3}

4. convergence\:\sum_{n=1}^{\infty}\frac{1}{4n+3}

5. convergence\:\sum_{n=1}^{\infty}\frac{n+2}{n^{2}+1}

5. convergence\:\sum_{n=1}^{\infty}\frac{n+2}{n^{2}+1}

6. convergence\:\sum_{n=1}^{\infty}\frac{1}{4n+5}

6. convergence\:\sum_{n=1}^{\infty}\frac{1}{4n+5}

7. convergence\:\sum_{n=1}^{\infty}\frac{1}{\sqrt{n(n+1)}}

7. convergence\:\sum_{n=1}^{\infty}\frac{1}{\sqrt{n(n+1)}}

8. convergence\:\sum_{n=1}^{\infty}\frac{3n+2}{n(n+1)}

8. convergence\:\sum_{n=1}^{\infty}\frac{3n+2}{n(n+1)}

9. convergence\:\sum_{n=1}^{\infty}\sin(\frac{2}{n})

9. convergence\:\sum_{n=1}^{\infty}\sin(\frac{2}{n})

10. convergence\:\sum_{n=1}^{\infty}\frac{30n^{2}+1}{10n^{3}+n}

10. convergence\:\sum_{n=1}^{\infty}\frac{30n^{2}+1}{10n^{3}+n}

Answers

Series

Convergence Tests

Limit Comparison Test

1. \mathrm{diverges}

2. \mathrm{diverges}

3. \mathrm{diverges}

4. \mathrm{diverges}

5. \mathrm{diverges}

6. \mathrm{diverges}

7. \mathrm{diverges}

8. \mathrm{diverges}

9. \mathrm{diverges}

10. \mathrm{diverges}