Convergent and Divergent Sequences

Front

What is a convergent sequence?

Back

A sequence that approaches a specific limit as the number of terms increases.

Front

What is a divergent sequence?

Back

A sequence that does not approach any limit as the number of terms increases.

Front

What does it mean for a sequence to converge to a limit?

Back

It means that as the terms of the sequence progress, they get arbitrarily close to a specific value.

Front

Give an example of a convergent sequence.

Back

The sequence 1/n converges to 0 as n approaches infinity.

Front

Give an example of a divergent sequence.

Back

The sequence n (where n = 1, 2, 3, ...) diverges to infinity.

Front

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

Back

The limit is 0.

Front

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

Back

The sequence diverges; it does not approach any limit.

Front

How can you determine if a sequence converges or diverges?

Back

By analyzing the behavior of the sequence as n approaches infinity.

Front

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

Back

The limit is 0.

Front

What is the limit of the sequence 3 + 1/n as n approaches infinity?

Back

The limit is 3.