Proof: Sequence {sqrt(n+1)-sqrt(n)} Converges to 0 | Real Analysis Exercises

[@WrathofMath]

Check out more exercises in my Real Analysis Exercises playlist! kzbin.info/aero/PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC

[@vladkruto9469]

I like your slow and calm voice. Listening feels much more enjoyable

[@WrathofMath]

Thanks Vlad! I try to be very clear and easy to understand in my speech. Let me know if you ever have any video requests!

[@vladkruto9469]

@@WrathofMath I know that you do graph theory. I wondered if you also do automata theory, formal languages and such?

[@tyund]

I think you've made a mistake, you should find a value less than the original root n expression to keep the inequality, duplicating root n+1 instead of n. If not you could just replace the expression with any value bigger than one to proof this affirmation.

[@InexorableVideos]

You're right.

[@prettylittlelife3735]

yes, i agree with you

[@antoniwalburg47]

We could also do 1/sqrt(n+1) + sqrt(n) < 1/sqrt(n+1) < E

[@matthewthompson6455]

Instead of N > (1/4E^2) , could we have chosen N = (1/4E^2) instead ?

[@s.k.subasinghe1138]

thank you very much! the thing is can we use 1/ sqrt(n) instead of 1/2sqrt(n) when defining big N ?

[@user-zu6ts5fb6g]

Yes

[@aashsyed1277]

thanks so much!

[@WrathofMath]

My pleasure!

[@christydevaraj8411]

It is divergent in p series how can u explain

[@harrywang6792]

I was thinking about that too. Until I realized that you are not supposed to treat it as a telescoping series and cancel terms across different sums. In rigorous rearranging terms or calculating terms in different orders can change the result of the final answer in some series, and produce a wrong answer. So you have to work with individual terms in the sum. Checkout this video why you can't rearrange terms: kzbin.info/www/bejne/baC6fpSEnJl4sNk&ab_channel=JimFowler

[@BharatVicharVimarsh]

Sir if possible please make a series of bs ms maths

[@MaxBryzgalov]

Lol that was my hw in uni

[@WrathofMath]

Thanks for watching, hope it was helpful!

[@dhanushreevb3250]

Nice sir

[@WrathofMath]

Thank you!

[@bradx3827]

It’s like Sal Khan but better!

[@WrathofMath]

Thank you! One day I may have as many videos as Khan Academy has now, and it will be a tremendous occasion! Perhaps we'll be 100 videos into a series on the algebra of knots by then.

[@RohitKumar-jv1is]

I have a doubt

[@RohitKumar-jv1is]

Please help me out

[@RohitKumar-jv1is]

I have my exam on 24th

[@WrathofMath]

Thanks for watching, what's your question?

[@RohitKumar-jv1is]

I have texted you on insta .. can you please check that