Understanding and applying geometric series

What best describes the following infinite geometric series:

1/3 - 1/9 + 1/27 - 1/81 + ...

• the sum does not exist

• the sum exists

• Arithmetic

• Geometric

• Sequence

• Series

Evaluate the infinite series described: 

• 20/3
• No Sum
• 21/5
• 4/3

The sum of an infinite Geometric series is given by:

• 
• 
• 
• 

 $1\ +\frac{4}{3}+\left(\frac{4}{3}\right)^2+\left(\frac{4}{3}\right)^3+...$  

Does the following infinite geometric series converge or diverge?

• Converge

• Diverge

What best describes the following infinite geometric series:

1/3 - 1/9 + 1/27 - 1/81 + ...

• Diverges

• Converges

Find the sum:  100 + 40 + 16 + 6.4 + ...

• 250
• 166.67
• 164.96
• Infinity

Find the sum of the infinite geometric series, if it exists:
200 - 100 + 50 - 25 +

• Does not exist
• 400/ 3
• 3 / 400

• -25
• 25
• 30
• The series has no sum

Determine if the series converges or diverges

• Converges
• Diverges