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Convergence Tests Comparison Test Worksheets

Series

Convergence Tests

Comparison Test

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answers

Series

Convergence Tests

Comparison Test

1. \mathrm{diverges}

2. \mathrm{converges}

3. \mathrm{converges}

4. \mathrm{converges}

5. \mathrm{converges}

6. \frac{11}{18}

7. \mathrm{converges}

8. \mathrm{converges}

9. \mathrm{converges}

10. \mathrm{converges}