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Topic: on real part of [(1+isqrt(7))/2]^n
Replies: 20   Last Post: Feb 15, 2014 5:52 AM

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quasi

Posts: 10,232
Registered: 7/15/05
Re: on real part of [(1+isqrt(7))/2]^n
Posted: Feb 15, 2014 4:29 AM
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>konyberg
>
>|a_n| = |(sqrt(2))^n * cos(n*acos(sqrt(2)/4))|
>
> = (sqrt(2))^n * |cos(n*acos(sqrt(2)/4))|
>
>where |cos(n*acos(sqrt(2)/4))| can be considered as a "constant"
>different from 0.


Certainly not!

Different from 0 doesn't mean it can be considered as a "constant".

For example, how do you know that there aren't infinitely positive
integers n such that

|cos(n*acos(sqrt(2)/4))| < 1/sqrt(2)^n

??

You don't.

>Conclusion: The limit |a_n| goes to infinity as n goes to
>infinity.


No, it's not even close to a proof.

quasi



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