Suppose $\sum \left|a_n\right|$ diverges. What can you conclude about $\sum a_n$?

Classify ${\sum }_{n=1}^{\infty }{\left(-1\right)}^{n+1}\frac{3n^2}{7n^2+9}$.

What does it mean for a series $\sum a_n$ to converge CONDITIONALLY?

Can a series whose terms are all POSITIVE converge conditionally?

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n{n}^2}{9^n}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$.

Classify ${\sum }_{n=1}^{\infty }{\left(-1\right)}^n\frac{n^2}{5n^2+7}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^{3/4}}$.

Classify ${\sum }_{n=1}^{\infty }\frac{\cos \left(3n\right)}{n^{3/2}}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{\sqrt{n}}$.

Which statement about a series $\sum a_n$ is TRUE? (Consider ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n}$ as a test case.)

Classify ${\sum }_{n=1}^{\infty }{\left(-1\right)}^{n+1}\frac{n^2}{9n^2+7}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}{n}^2}{5^n}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}{n}^2}{6^n}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}{n}^2}{8^n}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}{n}^2}{7^n}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n{7}^n}{n^2}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{n^{4/3}}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{n^{3/2}}$.

Classify ${\sum }_{n=1}^{\infty }\frac{\sin \left(2n\right)}{n^2}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{n^2}$.

Classify ${\sum }_{n=1}^{\infty }\frac{\cos n}{n^{3/2}}$.

Classify ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n}$.

Classify ${\sum }_{n=1}^{\infty }{\left(-1\right)}^n\frac{5n^2}{6n^2+11}$.