(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to find the order of convergence of the following sequence

[itex]b_n = \left( \frac{5}{6} \right)^{n^2} [/itex]

I have numerically tested that it has to be a real number between 1 and 2, but I can't find it exactly.

I also have this doubt: does every sequence have an order of convergence? (a real number [itex]p [/itex] such that [itex]| b_{n+1}/b_{n}^p|[/itex] converges to a non-zero constant )

2. Relevant equations

3. The attempt at a solution

Here http://translate.google.com/transla...xactas.wordpress.com/2011/08/29/tp-1-ej-1-3/" are my futile attempts at solving it.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Order of convergence of sequence

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