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Convergence Tests Geometric Series Test Worksheets

Series

Convergence Tests

Geometric Series Test

1. convergence\:\sum_{n=0}^{\infty}\frac{1}{2^{n}}

1. convergence\:\sum_{n=0}^{\infty}\frac{1}{2^{n}}

2. convergence\:\sum_{n=0}^{\infty}\frac{1}{e^{n}}

2. convergence\:\sum_{n=0}^{\infty}\frac{1}{e^{n}}

3. convergence\:\sum_{n=0}^{\infty} (-1)^{n}

3. convergence\:\sum_{n=0}^{\infty} (-1)^{n}

4. convergence\:\sum_{n=0}^{\infty}2^{n}

4. convergence\:\sum_{n=0}^{\infty}2^{n}

5. convergence\:\sum_{n=0}^{\infty} (\frac{e}{10})^{n}

5. convergence\:\sum_{n=0}^{\infty} (\frac{e}{10})^{n}

6. convergence\:\sum_{n=0}^{\infty} (\frac{2}{3})^{n}

6. convergence\:\sum_{n=0}^{\infty} (\frac{2}{3})^{n}

7. convergence\:\sum_{i=0}^{\infty} (\frac{1}{5})^{i}

7. convergence\:\sum_{i=0}^{\infty} (\frac{1}{5})^{i}

8. convergence\:\sum_{n=0}^{\infty} (\frac{e}{\pi})^{n}

8. convergence\:\sum_{n=0}^{\infty} (\frac{e}{\pi})^{n}

9. convergence\:\sum_{n=0}^{\infty} \frac{1}{3^{n}}

9. convergence\:\sum_{n=0}^{\infty} \frac{1}{3^{n}}

10. convergence\:\sum_{n=0}^{\infty} 0.5^{n}

10. convergence\:\sum_{n=0}^{\infty} 0.5^{n}

Answers

Series

Convergence Tests

Geometric Series Test

1. 2

2. \frac{e}{e-1}

3. \mathrm{diverges}

4. \mathrm{diverges}

5. \frac{10}{10-e}

6. 3

7. \frac{5}{4}

8. \mathrm{converges}

9. \frac{3}{2}

10. 2