Question

a sequence can't converge ...to more than limit point
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Answer 1

Answer:

a sequence can't converge ...to more than limit point

Answer 2

Concept introduction:

Theorem: Limits' Uniqueness There can only be one limit to which a series may converge. Theorem There are no unbounded convergent sequences.

Explanation:

Given that, a sequence can't converge ...to more than limit point.

We have to find, why a sequence can't converge ...to more than limit point.

According to the question,

Sequences can only converge to one limit since the notion of convergence makes it possible to demonstrate that a limit is distinct if it exists. A sequence, however, could contain a number of convergent subsequences with unique bounds. This cannot be done. Convergence suggests that the limit is singular.

Final Answer:

Sequences can only converge to one limit since the notion of convergence makes it possible to demonstrate that a limit is distinct if it exists.

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