1. What is an infinite sequence?
2. Which statement correctly describes convergence of a sequence?
3. For which values of r does the sequence r^n converge?
What is an infinite sequence in mathematics?
An ordered list of numbers indexed by positive integers or another integer set.
When does a sequence converge to a limit L?
When its terms become arbitrarily close to L as n approaches infinity.
What happens if a sequence has no finite limit?
The sequence diverges.
For which values of r does the sequence r^n converge?
For all r with -1 < r ≤ 1.
What is the limit of the sequence r^n when -1 < r < 1?
The limit is 0.
What is the limit of the sequence r^n when r = 1?
The limit is 1.
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