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

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We prove the sequence ( sqrt(n+1) - sqrt(n) ) converges to 0. Or, said in terms of limits, the limit of sqrt(n+1) - sqrt(n) as n approaches infinity is equal to 0. We prove this using the epsilon definition of the limit of a sequence, the Archimedean principle, and conjugates! #RealAnalysis

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

vladkruto

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

matthewthompson

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

antoniwalburg

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

s.k.subasinghe

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.

tyund

It is divergent in p series how can u explain

christydevaraj

Sir if possible please make a series of bs ms maths

BharatVicharVimarsh

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