How many terms of ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ are needed to GUARANTEE that the partial sum approximates the total to within $\frac{1}{200}$?

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ converges to $S$. If $S_7$, the sum of the FIRST 7 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_7\right|$?

How many terms of ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ are needed to GUARANTEE that the partial sum approximates the total to within $\frac{1}{10}$?

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^2}$ converges to $S$. If $S_8$, the sum of the FIRST 8 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_8\right|$?

How many terms of ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^2}$ are needed to GUARANTEE that the partial sum approximates the total to within $\frac{1}{10}$?

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ converges to $S$. If $S_5$, the sum of the FIRST 5 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_5\right|$?

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

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^2}$ converges to $S$. If $S_5$, the sum of the FIRST 5 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_5\right|$?

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

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

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^2}$ 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 ${\sum }_{n=1}^{\infty }{\left(-1\right)}^{n+1}\frac{4n}{n+4}$ converge?

Does ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^{4/3}}$ converge absolutely, converge conditionally, or diverge?

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^2}$ converges to $S$. If $S_6$, the sum of the FIRST 6 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_6\right|$?

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{n!}$ converges to $S$. If $S_4$, the sum of the FIRST 4 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_4\right|$?

Does ${\sum }_{n=1}^{\infty }{\left(-1\right)}^n\frac{7n}{n+9}$ converge?

A convergent alternating series has a NEGATIVE first term and terms that decrease in absolute value. $S_5$ is used to approximate the sum $S$. What is true of $S_5$?

Does ${\sum }_{n=1}^{\infty }{\left(-1\right)}^n\frac{9n}{n+6}$ converge?

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

The series ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ converges to $S$. If $S_8$, the sum of the FIRST 8 TERMS, is used to approximate $S$, what bound does the alternating series bound give for $\left|S-S_8\right|$?

How many terms of ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{n^3}$ are needed to GUARANTEE that the partial sum approximates the total to within $\frac{1}{1000}$?

Does ${\sum }_{n=1}^{\infty }{\left(-1\right)}^n\frac{7n}{n+1}$ converge?

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

A convergent alternating series has a NEGATIVE first term and terms that decrease in absolute value. $S_8$ is used to approximate the sum $S$. What is true of $S_8$?