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Question Number 95325 by ~blr237~ last updated on 24/May/20

 lim_(n→∞)     (1/n)HCF(20,n) = 0       ?

limn1nHCF(20,n)=0?

Commented by mr W last updated on 24/May/20

1≤HCF(20,n)≤20 for n≥20  (1/n)≤((HCF(20,n))/n)≤((20)/n)  lim_(n→∞) (1/n)≤lim_(n→∞) ((HCF(20,n))/n)≤lim_(n→∞) ((20)/n)  0≤lim_(n→∞) ((HCF(20,n))/n)≤0  ⇒lim_(n→∞) ((HCF(20,n))/n)=0

1HCF(20,n)20forn201nHCF(20,n)n20nlimn1nlimnHCF(20,n)nlimn20n0limnHCF(20,n)n0limnHCF(20,n)n=0

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