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-

Question Number 481 by 123456 last updated on 12/Jan/15

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}} ?