Infinite Limits of Sequences at Infinity

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2025-03-20 23:22

In this video I go over the notation and precise definition for sequences that diverge to infinity when the number of terms go to infinity. The precise definition states that the limit of a sequence approaches infinity if for every positive number M there is a corresponding integer N such that the terms of the sequence are greater than M whenever the n-th term is greater than N. Just as with limits in general, the infinite limit of a function at infinity is the same as that for a sequence except that we are dealing with integer values for the domain of sequences.

#math #limits #sequences #algebra #education

5 Infinite Limits of Sequences at Infinity.jpeg

Timestamps

Notation for infinite limits: 0:00
Definition 3: Precise definition for an infinite limit at infinity: 0:36
Definition for sequences is similar to functions: 1:18
Graphing infinite limit at infinity for functions: 1:45
- Graphing corresponding infinite limit at infinity for sequences: 3:30
Infinite limits at infinity are said to be divergent or diverges to infinity: 5:25