BC 9.12 (error in alternating series) and 9.13 ratio test

Which of the following is an approximation for the series $\sum_{n=1}^{\infty}\frac{\left(-1\right)^n}{n^3}$   with an error less than  $\frac{1}{20}$  ?

•  $-\frac{7}{8}$  

•  $\frac{9}{8}$  

•  $\frac{1}{8}$  

•  $-\frac{1}{8}$  
  

Which of the following is an approximation for the series $\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{n!}$   with an error less than  $\frac{1}{20}$  ?

•  $\frac{8}{3}$  

•  $\frac{1}{3}$  

•  $\frac{7}{3}$  

•  $\frac{13}{6}$  
  

Which of the following is an approximation for the series $\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{2n+1}$   with an error less than  $\frac{1}{6}$  ?

•  $\frac{23}{15}$  

•  $\frac{13}{15}$  

•  $\frac{19}{15}$  

•  $\frac{17}{15}$  
  

Which of the following is an approximation for the series $\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{2^{n-1}}$   with an error less than  $\frac{1}{10}$  ?

•  $\frac{31}{8}$  

•  $\frac{27}{8}$  

•  $\frac{17}{8}$  

•  $\frac{11}{8}$   
  

What degree of partial sum would approximate the sum of the series $\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{3n^2+8}$   with an error less than  $\frac{1}{200}$  ?

•  $8$  

• 9 

• 7

• 10

What degree of partial sum would approximate the sum of the series $\sum_{n=2}^{\infty}\frac{\left(-1\right)^n}{2n-3}$   with an error less than  $\frac{1}{200}$  ?

• 101

• 102

• 100

• 103

What degree of partial sum would approximate the sum of the series $\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{2^n+15}$   with an error less than  $\frac{1}{100}$  ?

• 5

• 6

• 7

• 4

How many terms would be necessary to approximate the sum of the series $\sum_{n=2}^{\infty}\frac{\left(-1\right)^n}{4^n}$   with an error less than  $\frac{1}{100}$  ?

• 2

• 3

• 5

• 4

How many terms would be necessary to approximate the sum of the series $\sum_{n=5}^{\infty}\frac{\left(-1\right)^n}{2n+1}$   with an error less than  $\frac{1}{100}$  ?

• 44

• 46

• 49

• 45

If a 5th degree partial sum is used to approximate the series $\sum_{n=2}^{\infty}\frac{\left(-1\right)^n}{n^2+2n-1}$ , what is the 1st omitted term? 

•  $\frac{1}{47}$  
  

•  $\frac{1}{34}$  

•  $-\frac{1}{34}$  

•  $\frac{1}{23}$