What does it mean for a sequence to converge?
Understand the Problem
The question is asking for the definition or explanation of the concept of convergence in the context of a sequence in mathematics. It is likely looking for a description of what it means for the terms of a sequence to approach a specific value as the sequence progresses.
Answer
A sequence converges if its limit exists as n → ∞.
The final answer is that a sequence converges if the limit of the sequence exists as n approaches infinity.
Answer for screen readers
The final answer is that a sequence converges if the limit of the sequence exists as n approaches infinity.
More Information
In mathematical terms, a sequence converges to a limit L if for every positive number ϵ, there exists a positive integer N such that for all n > N, the absolute difference between the sequence term and L is less than ϵ.
Tips
A common mistake is assuming a sequence converges if it just doesn't grow indefinitely. Always check if the limits exist.
Sources
- What does it mean for a sequence to converge? - socratic.org
- Convergent Sequence -- from Wolfram MathWorld - mathworld.wolfram.com
- Convergence of a Sequence - kristakingmath.com
