(a) Prove that if 0<a<2, then a<2 <2. (b) Prove that the sequence , , converges. (c) Find the limit of the sequence. Thanks.
Last edited by khatz; July 19th 2009 at 08:18 PM.
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Originally Posted by khatz (a) Prove that if 0<a<2, then a<2 <2. It isn't true! Must be a typo somewhere.
For (b) show that the sequence is increasing (I wont show that here) and bounded. Clearly so assume that for some n. Then so for all n and is thus bounded.
Originally Posted by AlephZero It isn't true! Must be a typo somewhere. Yes, it should be 2sqrt(a).
Originally Posted by khatz Yes, it should be 2sqrt(a). Still not true! Counterexample:
Originally Posted by khatz (a) Prove that if 0<a<2, then a<2 <2. (c) Find the limit of the sequence. Thanks. Considering what it leads onto, I think (a) should be (a) Prove that if , then For (c), if the limit it exists we can say that So what can you say about ?
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