Understanding Sequences and Limits

The video tutorial introduces a sequence that alternates in sign and decreases in magnitude. It explains how to graph the sequence on a coordinate plane, defines the sequence formula, and explores its behavior as it approaches infinity. The tutorial concludes by discussing the concept of limits and convergence, explaining that the sequence converges to zero as the number of terms increases.

What is the first term of the sequence described in the video?

• -1/2

• 1

• -1/4

• 1/3

How does the sequence alternate in terms of sign?

• Positive, Positive, Negative

• Negative, Negative, Positive

• Negative, Positive, Negative

• Positive, Negative, Positive

What is the value of a sub n when n equals 3?

• -1/4

• -1/2

• 1

• 1/3

What does the graph of the sequence suggest about the terms as n increases?

• They oscillate without pattern

• They get closer to zero

• They remain constant

• They move away from zero

What is the explicit formula for a sub n?

• n/(-1)^(n+1)

• (-1)^(n+1)/n

• (-1)^n/n

• 1/n

What happens to the sequence as n approaches infinity?

• It converges to zero

• It becomes undefined

• It diverges to infinity

• It oscillates indefinitely

What is the behavior of the numerator in the sequence's formula as n increases?

• It becomes zero

• It remains constant

• It oscillates between 1 and -1

• It increases indefinitely

What is the condition for a sequence to be considered convergent?

• It must remain constant

• It must reach infinity

• It must approach a specific value

• It must oscillate

If a sequence does not approach a specific value, what is it considered?

• Constant

• Divergent

• Undefined

• Convergent

What is the limit of the sequence as n approaches infinity?

• -1

• 0

• Infinity

• 1