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Results tagged with sequences-and-series
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user 80790
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
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Supremum of $ a_n = a_{n-1}^3 - a_{n-2} $
Let $a_1=0$ and let $ - \ln(2) < a_2 < \ln(2) $
Define
$$ a_n = a_{n-1}^3 - a_{n-2} $$
Then
$$ \sup_{n>2} a_n = a_2 $$
And
$$ \inf_{n>2} a_n = - a_2 $$
How to prove that ?
- 769