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Results tagged with sequences-and-series
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user 144027
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.
4
votes
Simple-looking sequences $A$ and $B$ defined by a complementary equation
Your formula is true. From the construction of the sequences $a_n$ and $b_n$, it is not hard to see that for all $n \in \mathbb{N}$:
\begin{equation}
\begin{cases}
b_{n + 1} - b_n & \in \left\lbrace …
- 41