05/03/2009, 10:42 PM
(04/13/2009, 05:01 PM)bo198214 Wrote:andydude Wrote:\( \eta < \text{srt}_{k+1}({k+1}) < \text{srt}_k(k) \) for all \( k \ge 5 \) by lemma (4) and lemma (5).
... In the limit, the squeeze theorem and completeness should guarantee that the limit exists and converges to \( \eta \).
Is this right?
I dont think so. When the sequence is decreasing and bounded it has a limit. But this limit could be probably bigger than \( \eta \). Or did I overlook something?
\( \eta < \text{srt}_{k+1}({k+1}) < \text{srt}_k(k) \) for all \( k \ge 5 \)
so the limit must be eta when lim k = oo because the rule is < and not =< , i think bo has overlooked that !?!
or did i miss something ?