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Let $a,b,c \ge 0$ with a series such that

$a_1 = 0$

$a_i \le a + b(c + a_{i-1})a_{i-1}$

I am looking for an upper bound on $a_i$ (tight as possible) in terms of $a$,$b$,$c$ and $i$.

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    Since the rhs is increasing in $a_{i-1}$, shouldn't $a_i = a+b(c+a_{i-1})a_{i-1}$ be the extreme case?2012-05-31
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    This looks like a sequence, not a series, to me. Am I mistaken?2012-05-31
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    @mixedmath I can't remember any reference now but I have seen that usage of "series" before.2012-05-31
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    @kloop Do you mean asymptotic bound?2012-05-31
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    @A.D. no, I mean something like the following: http://math.stackexchange.com/questions/150299/bound-on-recursive-series2012-05-31
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    @Ilya, yes, that would be the extreme case, I believe, so without loss of generality, we can assume an equality sign there.2012-05-31

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