(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume [itex] a_n [/itex] is a bounded sequence with the property that every convergent sub sequence of [itex] a_n [/itex] converges to the same limit a. Show that

[itex] a_n [/itex] must converge to a.

3. The attempt at a solution

Could I do a proof by contradiction. And assume that [itex] a_n [/itex] does not converge

to a. but then this would imply that there would be a sub sequence that did not converge

to a and this is a contradiction because I could pick a sub sequence that converged to the same thing that [itex] a_n [/itex] did

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# Convergence of a sequence.

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