anonymous
  • anonymous
A killer problem. If \(a_0=1\) and:\[a_n=a_{\frac{n}{2}}+a_{\frac{n}{3}}+a_{\frac{n}{6}}\]Find the convergence or divergence of \(\frac{a_n}{n}\).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
This is complex analysis, by the way.
anonymous
  • anonymous
Or real. I actually have no idea.
anonymous
  • anonymous
I'm not sure I understand the notation.... \[a_{\frac{n}{2}}\] only makes sense for an even "n"...

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anonymous
  • anonymous
Yes, therefore it's only defined that \(n\mid\left(\frac{n}{2},\frac{n}{3}\right)\in\mathbb Z\).
anonymous
  • anonymous
this would diverge cuz its a harmonic series 1/n diverges i would use the comparison test, and conclude that the overall series diverges cuz ur comparing it with 1/n with diverges cuz p<1 i hope im right lol
anonymous
  • anonymous
It still doesn't make sense to me. The first term that would work is \[a_{\frac{n}{6}} = a_3 + a_2 + a_1 \] And we don't know any of those terms on the right.
anonymous
  • anonymous
My question as well; but the problem is correctly written, so!
anonymous
  • anonymous
Also, it's not harmonic. It's way too erratic.
anonymous
  • anonymous
lol well idk then, what class is this for? lmk when u find an answer im curious
anonymous
  • anonymous
Is this problem from a textbook or a problem set made up by a professor?
anonymous
  • anonymous
Setup by a professor. This problem was for chaos theory and stochastic analysis.
anonymous
  • anonymous
lol i havent even hit this yet, im still in calc 2 haha
anonymous
  • anonymous
Interesting. I apologize that I'm not of much help, I really just don't understand the way it's written or what exactly it's asking for. It doesn't make sense to me to have a sequence whose terms are only defined for certain values of n.
anonymous
  • anonymous
I don't know if @JamesJ is around right now but if so, maybe he can take a look. I might just be crazy or overlooking something.
anonymous
  • anonymous
It's a very weird problem.
anonymous
  • anonymous
Not well posed, but clearly divergent. If the new term is the sum of three (if they exist) previous positive terms, the new terms keep getting bigger. Hard to converge if it does this.
anonymous
  • anonymous
It's \[\frac{a_n}{n} \]
anonymous
  • anonymous
I think I'm going in the right direction for proof of existence of convergence of \(\frac{a_n}{n}\):\[f(x)=6x\mid\forall\left(0
anonymous
  • anonymous
Alternatively, it might be possible to prove that this system is not mappable in any space.

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