Alternating Series Test for Convergence

Determine the convergence or divergence of  $\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n+1}}{n+1}$  

• Converges

• Diverges because it does not pass the first condition of AST:  $\lim_{n\rightarrow\infty}a_n=0$  

• Diverges because it does not pass the second condition of AST: $a_{n+1}\le a_n$  for all n

Determine the convergence or divergence of  $\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n+1}n}{3n+2}$  

• Converges

• Diverges because it does not pass the first condition of AST:  $\lim_{n\rightarrow\infty}a_n=0$  

• Diverges because it does not pass the second condition of AST: $a_{n+1}\le a_n$  for all n

Determine the convergence or divergence of  $\sum_{n=1}^{\infty}\frac{\left(-1\right)^nn}{\ln\left(n+1\right)}$  

• Converges

• Diverges because it does not pass the first condition of AST:  $\lim_{n\rightarrow\infty}a_n=0$  

• Diverges because it does not pass the second condition of AST: $a_{n+1}\le a_n$  for all n

Determine the convergence or divergence of  $\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{n!}$  

• Converges

• Diverges because it does not pass the first condition of AST:  $\lim_{n\rightarrow\infty}a_n=0$  

• Diverges because it does not pass the second condition of AST: $a_{n+1}\le a_n$  for all n

Determine the convergence or divergence of  $\frac{3}{2}-\frac{2}{2}+\frac{3}{3}-\frac{2}{3}+\frac{3}{4}-\frac{2}{4}+...$  

• Converges

• Diverges because it does not pass the first condition of AST:  $\lim_{n\rightarrow\infty}a_n=0$  

• Diverges because it does not pass the second condition of AST: $a_{n+1}\le a_n$  for all n