Find the exact sum of ${\sum }_{n=1}^{\infty }5{\left(\frac{2}{5}\right)}^n$.

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

Apply the Ratio Test to ${\sum }_{n=1}^{\infty }\frac{5^n}{n!}$.

What does the nth-Term Test tell you about ${\sum }_{n=1}^{\infty }\frac{3n+2}{6n-31}$?

Does the sequence $a_n=\frac{5n}{e^n}$ converge, and if so to what limit?

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

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

What is the INTERVAL of convergence of ${\sum }_{n=1}^{\infty }\frac{{\left(x+1\right)}^n}{n{4}^n}$? Give your answer in interval notation.

Find the exact sum of ${\sum }_{n=3}^{\infty }2{\left(-\frac{3}{4}\right)}^n$.

What does the nth-Term Test tell you about ${\sum }_{n=1}^{\infty }\frac{6n^2+3}{7n^2-4n}$?

Find the exact sum of ${\sum }_{n=1}^{\infty }8{\left(-\frac{1}{4}\right)}^n$.

Apply the Integral Test to ${\sum }_{n=2}^{\infty }\frac{\ln n}{n}$. What is the conclusion?

What is the THIRD-degree Taylor polynomial for $f(x)=\ln x$ about $x=2$?

What is the INTERVAL of convergence of ${\sum }_{n=1}^{\infty }\frac{{\left(x-3\right)}^n}{n^2{2}^n}$? Give your answer in interval notation.

What does the nth-Term Test tell you about ${\sum }_{n=1}^{\infty }\frac{3n^2-3}{5n^2-4n}$?

Does the sequence $a_n=\frac{6\ln n}{n}$ converge, and if so to what limit?

Apply the Limit Comparison Test to ${\sum }_{n=1}^{\infty }\frac{3n^2+4}{5n^4-n}$ using $b_n=\frac{1}{n^2}$. What is the limit, and what does it establish?

Apply the Limit Comparison Test to ${\sum }_{n=1}^{\infty }\frac{6n+7}{4n^3-n}$ using $b_n=\frac{1}{n^2}$. What is the limit, and what does it establish?

Apply the Limit Comparison Test to ${\sum }_{n=1}^{\infty }\frac{9n^2+10}{6n^3-n}$ using $b_n=\frac{1}{n}$. What is the limit, and what does it establish?

What is the INTERVAL of convergence of ${\sum }_{n=1}^{\infty }\frac{{\left(x-1\right)}^n}{n{5}^n}$? Give your answer in interval notation.

Does ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{2^n}$ converge?

Find the exact sum of ${\sum }_{n=3}^{\infty }4{\left(\frac{4}{5}\right)}^n$.

Does the sequence $a_n=\frac{7n^2-4}{2n^2+5n}$ converge, and if so to what limit?

Find the exact sum of ${\sum }_{n=3}^{\infty }4{\left(-\frac{1}{3}\right)}^n$.

Apply the Limit Comparison Test to ${\sum }_{n=1}^{\infty }\frac{7n^2+8}{5n^3-n}$ using $b_n=\frac{1}{n}$. What is the limit, and what does it establish?

What is the THIRD-degree Taylor polynomial for $f(x)=\ln x$ about $x=1$?

What is the INTERVAL of convergence of ${\sum }_{n=1}^{\infty }\frac{{\left(x-1\right)}^n}{n{6}^n}$? Give your answer in interval notation.

Does the sequence $a_n=\frac{9n^2+4}{6n^2+5n}$ converge, and if so to what limit?

What does the nth-Term Test tell you about ${\sum }_{n=1}^{\infty }\frac{4n+6}{5n-71}$?

Apply the Ratio Test to ${\sum }_{n=1}^{\infty }\frac{n^2}{9^n}$.

Find the exact sum of ${\sum }_{n=1}^{\infty }2{\left(\frac{1}{6}\right)}^n$.

Apply the Ratio Test to ${\sum }_{n=1}^{\infty }\frac{n!}{2^n}$.

Does the sequence $a_n=\frac{3n^2-6}{9n^2+7n}$ converge, and if so to what limit?

What is the INTERVAL of convergence of ${\sum }_{n=1}^{\infty }\frac{{\left(x+3\right)}^n}{n^2{4}^n}$? Give your answer in interval notation.

Apply the Limit Comparison Test to ${\sum }_{n=1}^{\infty }\frac{5n+6}{8n^2-n}$ using $b_n=\frac{1}{n}$. What is the limit, and what does it establish?

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

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ converges to $S$. If $S_3$, the sum of the FIRST 3 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_3\right|$?

Does ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ converge?

What is the THIRD-degree Taylor polynomial for $f(x)=\frac{1}{x}$ about $x=5$?

What does the nth-Term Test tell you about ${\sum }_{n=1}^{\infty }\frac{7n+6}{5n-71}$?