5
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Bug introduced in 9.0.0 and fixed in 10.0.1

Limit[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n), n -> Infinity]

Mathematica (wrong) output:

0

But this is correct:

FullSimplify[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n)]
1

And also this is correct:

Limit[(Log[4]/(2*Log[2]))^(-1-2*n), n -> Infinity]
1
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7
  • 4
    $\begingroup$ Version 10.1 under Windows x64 gives 1 for the first input line. This is probably a bug that has been corrected. $\endgroup$
    – Mr.Wizard
    Commented May 22, 2015 at 10:10
  • $\begingroup$ Thank you, I tested it under version 10.0.0.0 $\endgroup$
    – Vaclav Kotesovec
    Commented May 22, 2015 at 10:17
  • 1
    $\begingroup$ Gives 0 in version 9.0.1, and returns unevaluated in previous versions. Looks like the bug was introduced in version 9. $\endgroup$
    – Oleksandr R.
    Commented May 22, 2015 at 11:22
  • $\begingroup$ Version 10.0.2 also gives 1. Can anyone test 10.0.1? $\endgroup$
    – Mr.Wizard
    Commented May 22, 2015 at 11:41
  • 1
    $\begingroup$ 10.0.1 gives 1. $\endgroup$
    – N.J.Evans
    Commented May 22, 2015 at 13:52

1 Answer 1

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1
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Summarizing the comments, this bug has been fixed as of version 10.0.1.

Limit[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n), n -> Infinity]    

(* 1 *)
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