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Convergence Tests Integral Test Worksheets - Download free PDFs

Series

Convergence Tests

Integral Test

1. convergence\:\sum_{n=0}^{\infty}\frac{1}{1+\sqrt{n}}

1. convergence\:\sum_{n=0}^{\infty}\frac{1}{1+\sqrt{n}}

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

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

3. convergence\:\sum_{n=1}^{\infty}\frac{1}{n^{2}-9}

3. convergence\:\sum_{n=1}^{\infty}\frac{1}{n^{2}-9}

4. convergence\:\sum_{n=6}^{\infty}\frac{1}{(n-3)(n-5)}

4. convergence\:\sum_{n=6}^{\infty}\frac{1}{(n-3)(n-5)}

5. convergence\:\sum_{n=2}^{\infty}\frac{\ln(n)}{n^{2}}

5. convergence\:\sum_{n=2}^{\infty}\frac{\ln(n)}{n^{2}}

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

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

7. convergence\:\sum_{n=1}^{\infty}\frac{\ln(n)}{n^{3}}

7. convergence\:\sum_{n=1}^{\infty}\frac{\ln(n)}{n^{3}}

8. convergence\:\sum_{n=2}^{\infty}\frac{1}{nn^{\frac{1}{3}}-n}

8. convergence\:\sum_{n=2}^{\infty}\frac{1}{nn^{\frac{1}{3}}-n}

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

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

10. convergence\:\sum_{n=2}^{\infty}\frac{1}{n\sqrt{\ln(n)}}

10. convergence\:\sum_{n=2}^{\infty}\frac{1}{n\sqrt{\ln(n)}}

Answers

Series

Convergence Tests

Integral Test

1. \mathrm{diverges}

2. \mathrm{diverges}

3. \mathrm{converges}

4. \mathrm{converges}

5. \mathrm{converges}

6. \mathrm{diverges}

7. \mathrm{converges}

8. \mathrm{converges}

9. \mathrm{diverges}

10. \mathrm{diverges}