proof or given a counter example: if {x_n } is a no limited sequence then exist a sub−sequence {x_(nk) } that lim_(n→0) (1/x


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Question Number 481 by 123456 last updated on 12/Jan/15
$proof or given a counter example: if {x_n } is a no limited sequence then exist a sub−sequence {x_(nk) } that lim_(n→0) (1/x_(nk) )=0$
$p r o o f o r g i v e n a c o u n t e r e x a m p l e :$ $i f {x_{n}} i s a n o l i m i t e d s e q u e n c e$ $t h e n$ $e x i s t a s u b - s e q u e n c e {x_{n k}} t h a t$ $\lim_{n \to 0} \frac{1}{x_{n k}} = 0$
Commented by prakash jain last updated on 13/Jan/15

$\lim_{n \to 0} \frac{1}{x_{n k}} = 0 do you mean sum of the sequence \frac{1}{x_{n k}} ?$
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