Let (sn) be a sequence that converges. (a) Show that if sn ? a for all...
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Let (sn) be a sequence that converges.
(a) Show that if sn ? a for all but finitely many n,then lim sn ? a.
(b) Show that if sn ? b for all but finitely many n,then lim sn ? b.
(c) Conclude that if all but finitely many sn belong to [a,b],then lim sn belongs to [a, b].
Let (sn) be a sequence that converges.
(a) Show that if sn ? a for all but finitely many n,then lim sn ? a.
(b) Show that if sn ? b for all but finitely many n,then lim sn ? b.
(c) Conclude that if all but finitely many sn belong to [a,b],then lim sn belongs to [a, b].
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Here first we prove the
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