If is a sequence and there is a such that for all , then can converge? We claim that if , then . For , , which is false. So it cannot be a contractive sequence?
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although this seems too simple.
Originally Posted by particlejohn If is a sequence and there is a such that for all , then can converge? Note that . Because if this was not the case then which is impossible. But as you showed . Let . Then for . Therfore the sequence is not Cauchy and therefore not convergent.
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