Question

State whether the sequence converges and, if it does, find the limit. $$(-1)^{n} \sqrt{n}$$

Name: Problem 11, Chapter 11: Calculus: One Variable
Uploaded: 2021-08-26T17:21:14-08:00
Duration: 1 min 38 s
Channel: Joy Carpio
Description: State whether the sequence converges and, if it does, find the limit. (-1)^n √(n)

   State whether the sequence converges and, if it does, find the limit.
$$(-1)^{n} \sqrt{n}$$

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 11, Problem 11

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Solved by Expert Joy Carpio

08/26/2021

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We want to find out if this sequence converges or not. Show more…

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State whether the sequence converges and, if it does, find the limit. $$(-1)^{n} \sqrt{n}$$

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Key Concepts

Sequence Convergence

Sequence convergence refers to the behavior of a sequence where the terms approach a specific value, known as the limit, as the index approaches infinity. For a sequence to converge, for any given small number ?, there must exist a stage beyond which all terms of the sequence are within ? distance of the limit.

Alternating Sequence

An alternating sequence is one in which the sign of each term alternates, typically due to a factor such as (-1)^n. This characteristic causes the sequence's terms to switch direction each step, which can complicate convergence analysis when combined with other varying factors.

Unbounded Growth

Unbounded growth describes a sequence that increases without limit in absolute value. When a sequence includes a term that grows without bound, such as ?n or n itself, this typically causes the sequence to diverge, as the values do not settle near any finite number.

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