Proof: Sequence 1/sqrt(n) Converges to 0 | Real Analysis
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- čas přidán 26. 08. 2024
- 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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thanks great explanation
Glad it was helpful!
Bro is there any way to use sandwich theorem for this?
easy to understand
Glad to hear it, thanks for watching!
Great video. What are you plans for when you finish your Real Analysis playlist?
Thank you! Maybe abstract algebra, or I might really get going on a standard Calculus I playlist.
@@WrathofMath Oh, Abstract Algebra is nice. Great job man, your channel is going places.
It sure is! Thanks for your support! Down the line, I hope to make more traditional lectures on these subjects, so rather than a bunch of standalone videos on the topic arranged in a playlist, there would be a smaller collection of longer lectures - all cohesive and tied together as you would get from attending a course. But that's very demanding, so I'll have to grow the channel more before I can afford the time!
Thank you for the this video
Thank you for this good video...keep going with good work.
Thank you - I will!
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?
Generally speaking, no. There just needs to be some N that works. So whether we say "that N exists past this number" or "that N is this number", the result is demonstrated. Sometimes it is more convenient or clear to specify how big N needs to be (with inequality) than to give a precise expression that works with equality.
@@WrathofMath thank you very much!
Amazing video once again! May I ask what the name of the song is at the end?
Thank you Alexia and I am glad you asked! At the end of my lessons, I often include music from my favorite songwriter who I wish more people knew about! That song is A Mask's Drawn smile, here is a link: crayonangel.bandcamp.com/track/a-masks-drawn-smile
@@WrathofMath Thank you for the info!!
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?
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Which app u were used please?