Proof: Sequence 1/sqrt(n) Converges to 0 | Real Analysis

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We will prove the sequence 1/sqrt(n) converges to 0. In other words, we're proving that the limit of 1/sqrt(n) as n approaches infinity is 0. We use the epsilon definition of a convergent sequence and the proof is straightforward, following the typical form of a convergent sequence proof.

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Комментарии
Автор

Can’t 1/sqrt(n) be negative since square roots could be equal to a negative number?

Jeff-lwlm
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Bro is there any way to use sandwich theorem for this?

SumanthGolagani
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in another video you made you set N = instead of N >, is there any difference? for example, if here we set N = 1/epsilon^2 instead of N > 1/epsilon^2, would things change?

tommasoc.
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Thanks for the great videos. In the proof, is it ok to start with the inequality (n > an expression involving ε which we found in our scratch work) and work towards building |{aₙ} - L| < ε by manipulating both sides? E.g. in this case could we start by assuming n > 1/ε² ⇒ 1/n < ε² ⇒ 1/√n̅ < ε ⇒ | 1/√n̅ - 0 | < ε. Would it always work?

EhsanAmini
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Amazing video once again! May I ask what the name of the song is at the end?

alexiadrey
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Great video. What are you plans for when you finish your Real Analysis playlist?

Koj
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Thank you for this good video...keep going with good work.

mahmoudalbahar