Thursday, August 8, 2019

real analysis - Show an+1=sqrt2+an,a1=sqrt2 is monotone increasing and bounded by 2; what is the limit?


Let the sequence {an} be defined as a1=2 and an+1=2+an.



Show that an 2 for all n, an is monotone increasing, and find the limit of an.




I've been working on this problem all night and every approach I've tried has ended in failure. I keep trying to start by saying that an>2 and showing a contradiction but have yet to conclude my proof.

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