Understanding the nth Term Test for Divergence

What is the primary purpose of the nth term test for divergence?

• To calculate the nth term of a series

• To determine if a series converges

• To find the sum of a series

• To check if a series diverges

If the limit of the nth term of a series as n approaches infinity is zero, what can be concluded?

• The series definitely converges

• The series definitely diverges

• The series oscillates

• No conclusion can be made

In the nth term test, if the limit of the nth term is not zero, what does this imply about the series?

• The series converges

• The series diverges

• The series is finite

• The series is undefined

What is the result of applying the nth term test to a series where the limit of the nth term is 5/3?

• The series converges

• The series diverges

• The series is geometric

• The series is arithmetic

How can you quickly determine if a series is geometric?

• By checking if the series has a common difference

• By identifying a common ratio

• By using the nth term test

• By calculating the sum of the series

What is the significance of the absolute value of the common ratio being less than one in a geometric series?

• The series is arithmetic

• The series is undefined

• The series converges

• The series diverges

When applying the nth term test, what conclusion can be drawn if the limit of the nth term is zero?

• The series diverges

• The series converges

• The series is geometric

• No conclusion can be drawn

What is the result of applying L'Hôpital's rule to a series where both the numerator and denominator approach infinity?

• The series is undefined

• The series is finite

• The series diverges

• The series converges

In the context of the nth term test, what does it mean if the numerator of a series grows faster than the denominator?

• The series is undefined

• The series diverges

• The series converges

• The series is finite

What is the outcome of the nth term test if the limit of the nth term is a non-zero constant?

• The series is finite

• The series is undefined

• The series diverges

• The series converges