Suppose (a_{n}) is bounded, and that every convergent subsequence of (a_{n}) has limit L. Prove that

Printable View

- Mar 17th 2013, 01:48 PMKanwar245Bounded Sequence
Suppose (a

_{n}) is bounded, and that every convergent subsequence of (a_{n}) has limit L. Prove that - Mar 17th 2013, 02:15 PMPlatoRe: Bounded Sequence
- Mar 17th 2013, 02:23 PMKanwar245Re: Bounded Sequence
Okay so from Bolzano-Wiererstrass since a_n is bounded, there exists atleast one convergent subsequence. Let that subsequence be a_n itself and we're done?

- Mar 17th 2013, 02:39 PMPlatoRe: Bounded Sequence
- Mar 17th 2013, 02:51 PMHallsofIvyRe: Bounded Sequence
- Mar 17th 2013, 02:54 PMKanwar245Re: Bounded Sequence