Series Practice

Determine the convergence of  $\sum_{n=1}^{\infty}\frac{\ln x}{x^2}.$  

• Converges

• Might Converge

• Diverges

• Can't be determined.

What is the sum of  $\sum_{n=1}^{\infty}\left(\frac{1}{n+1}-\frac{1}{n+3}\right).$  

•  $\frac{1}{4}$  

•  $\frac{1}{2}$  

•  $\frac{5}{6}$  

• diverges

Does the series  $\sum_{k=0}^{\infty}\frac{1}{k!}$  converge or diverge?

• Converge

• Diverge

Determine whether or not the series $\sum_{n=2}^{\infty}\left(-\frac{2}{7}\right)^n$   converges. If possible, give the sum. 

• converges to  $-\frac{2}{7}$  

• converges to  $\frac{4}{63}$  

• converges to  $\frac{4}{35}$  

• converges to  $\frac{7}{9}$  

• converges, but can't determine the sum
  

Does the series converge or diverge  $\sum_{n=0}^{\infty}\frac{11}{\sqrt{n^5+3}}$  ? 

• Converges

• Diverges

Does the series converge or diverge  $\sum_{n=1}^{\infty}\frac{n^2}{5^n}$ ?

• Converge

• Diverge

Does the series converge or diverge  $\sum_{n=1}^{\infty}\frac{n^n}{n!}$ ?

• Converge

• Diverge

Does the series  $\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+...$ converge or diverge?

• Converges

• Diverges

Does the series  $\frac{1}{4}-\frac{1}{9}+\frac{1}{16}-\frac{1}{25}+...$ absolutely converge, conditionally converge, or diverge?

• Absolutely converges

• Conditionally converges

• Diverges

Determine if the series $\sum_{n=1}^{\infty}\frac{\left(-1\right)^n}{\sqrt{3n+4}}$  converges absolutely, converges conditionally or diverges

• Converges absolutely

• Converges conditionally

• Diverges