Understanding Limits of Sequences

What does it mean for a sequence to converge?

• The sequence becomes infinite.

• The sequence oscillates indefinitely.

• The sequence approaches a specific real number.

• The sequence remains constant.

In the example of the sequence 1/n, what is the limit as n approaches infinity?

• 1

• Infinity

• Undefined

• 0

What happens to a sequence with a higher degree polynomial in the numerator compared to the denominator?

• It remains constant.

• It converges to a constant.

• It diverges to infinity.

• It converges to zero.

What is the limit of the sequence 1/2^n as n approaches infinity?

• Undefined

• Infinity

• 0

• 1

How does the sequence 7/6^n behave as n becomes very large?

• It converges to a constant.

• It diverges to infinity.

• It converges to zero.

• It oscillates indefinitely.

What is the behavior of the sequence e^n as n increases?

• It converges to zero.

• It diverges to infinity.

• It remains constant.

• It converges to a constant.

What is the limit of the sequence (-1)^n?

• It converges to zero.

• It diverges to infinity.

• It oscillates between -1 and 1.

• It converges to a constant.

How does the sequence (-1)^n/n behave as n becomes very large?

• It oscillates indefinitely.

• It converges to zero.

• It diverges to infinity.

• It remains constant.

What is the limit of a constant sequence where every term is the same number?

• The sequence becomes infinite.

• The sequence oscillates.

• The sequence converges to that number.

• The sequence diverges.

What is the result of applying a continuous function to the limit of a sequence?

• The function of the limit is undefined.

• The function of the limit diverges.

• The function of the limit is the same as the limit of the function.

• The function of the limit oscillates.