Thursday, 8 August 2013

analysis - How to show that limnto+inftynfrac1n=1?




I've spent the better part of this day trying to show from first principles that this sequence tends to 1. Could anyone give me an idea of how I can approach this problem?



limn+n1n


Answer



You can use AMGM.



1+1++1+n+nnn1/n1




12n+2nn1/n1


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