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Monotone Definition
Math
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Math
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Non-Monotonic
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18:45
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Pure Mathematics
A Cauchy Proof of Convergence for a Recursive Sequence
In this lecture, we prove the convergence of a recursively defined sequence using the Cauchy criterion, without relying on monotonicity or informal intuition. Beginning with a rational recursive definition, we analyze the behavior of successive differences and show that the sequence is Cauchy by establishing a uniform contraction. From this ...
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