Convergent Sequence Examples | Convergent Sequence | Sequence of real numbers: 08

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Sequence of Real Numbers | Range of Sequence | Bounded and Unbounded Sequence | Real Sequences : 01
Monotonic Sequence, Eventually Monotonic Sequence with examples | Sequence of real numbers : 02
Subsequence of a Sequence | Complimentary Pair of Subsequences | Sequence of real numbers : 03
Limit Point of a Sequence, Bolzano-Weierstrass Theorem | B-W Theorem | Sequence of real numbers: 04
Limit of a Sequence | Difference between Limit and Limit Point | Sequence of real numbers: 05
Convergent, Divergent and Oscillatory Sequence | Sequence of real numbers: 06
Convergent Sequence Examples | Convergent Sequence | Sequence of real numbers: 07

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[ramakantmaurya]

मुझे लगता है कि Real Analysis इससे ज्यादा आसान कोई समझा ही नहीं सकता मानना पड़ेगा सरजी वाह you are great

[PandeyTheSystem]

The way of your teaching is absolutely fantastic...you made any topic so easy to understand with simple and clear words...Sir i am a student follows your ..i request you to increase no. Of lecture per week...hope you consider it📝📝

[dcreations]

Sir your teaching way makes questions easier to understand and I would say your voice is also amazing ❤

[ashishmehta]

Aap jaise teacher ki jarurat Please AAP YouTube pr padaye...

[daniaaldanishlak]

Sir you are one of the greatest teachers I Have ever seen!!!!
You are an Amazing teacher!!!

[half-soul]

Hello everyone for those who had the doubt in example 5, I've resolved it finally after so many days haha. These are the steps to proceed.

Sir, has already shown the case for Monotonically Decreasing case when we take + sign. But, - is also possible as pointed out by many students.

Similarly, when we take - sign we get a Monotonically Increasing sequence.
i.e- a(n)<=a(n+1)
In the above equation put the value of a(n+1) from question and after simplification, we will get:
a(n)<=+√2 i.e- We get the higher bound for a M.Increasing sequence and also from question a(1)>0 and it's still bounded by a(1) regardless. Hence, it is bounded and monotonically increasing. Therefore, the limit exists.
The steps to find the limit are the same as in the video.

[praveenkumarbrathod]

Thanks a lot sir as always bravo explanation and no one matches to you and with great effort to understand us is more than laudable 🌹🌹

[arvindKumar-mbnw]

You are best teacher for higher mathematics

[vivekpareek]

Thank you sir very good and best videos for real analysis

[kamalsubba]

Very good lecture I ever watched job sir expecting even more vedios

[harshitakesharwani]

Thnk u so much sir for explaining it so understand every single word!!!

[jainshikhar]

Good morning sir🌞
One again your teaching skills mesmerized me and a lot of students like me.🙏
You are such a great teacher sir🙏

[samtapareek]

Thank you sir, I really understand the concepts of sequence. I want more mixed questions for sequence. Again, thank you sir👍👍

[shubhamjoshi]

Sir You explain it so well .
Sir please explain one example to prove two sequence convergence to a common limit..

[vivekpathak]

examine the boundedness of the following sequence 1- { n^1/n}
2- f(n), where f(n) = 1/2^n-1.
Sir give answer

[tiyaroy]

the way you teach is absolutely amazing Sir, I have no doubts so far...please upload the videos on further topics as our exams are in 10 days

[Manjot_duggal]

Well explained, all the doubts are clear now✨

[PriyaYadav-heij]

Thank you sir Iam more excited for this video

[bikrambhai---yt.]

inke jesa koi nehi pada sakta❤ love you sir

[gourav_shandilya]

Thank you sir ji 🙏🙏 acche se clear karne ke liye