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Results tagged with sequences-and-series
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user 18086
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.
2
votes
Repeatedly indexing into an $\infty$-sequence of integers
Suppose a sequence $s_k = (a_1, a_2, \ldots)$ has $s_k = s_{k+1}$. Then $a_i = a_{a_i}$, and by injectivity of $f$ (and hence iterations of $f$), we have $a_i = i$. So there is just one fixed sequence …
- 1,887
1
vote
Proving a sequence of integrals increases (iterated minimax distributions)
Use Jensen's inequality and induction on $n$.
Let $\phi_c(z) = (1- (1 - z)^c)^c$
, so that $\phi_c(F_i) = F_{i+1}$. As you noted, $\phi = f \circ f$, where $f(z) = (1-z)^c$. $f$ is convex for $0 \le …
- 1,887