Question Number 481 by 123456 last updated on 12/Jan/15
$${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:\left\{{x}_{{n}} \right\}\:{is}\:{a}\:{no}\:{limited}\:{sequence} \\ $$$${then} \\ $$$${exist}\:{a}\:{sub}−{sequence}\:\left\{{x}_{{nk}} \right\}\:{that} \\ $$$$\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}_{{nk}} }=\mathrm{0} \\ $$
Commented by prakash jain last updated on 13/Jan/15
$$\:\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}_{{nk}} }=\mathrm{0}\:\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}\frac{\mathrm{1}}{{x}_{{nk}} }? \\ $$