# Wrong Limit in Mathematica 10.0.0

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

• Version 10.1 under Windows x64 gives 1 for the first input line. This is probably a bug that has been corrected. May 22 '15 at 10:10
• Thank you, I tested it under version 10.0.0.0 May 22 '15 at 10:17
• Gives 0 in version 9.0.1, and returns unevaluated in previous versions. Looks like the bug was introduced in version 9. May 22 '15 at 11:22
• Version 10.0.2 also gives 1. Can anyone test 10.0.1? May 22 '15 at 11:41
• 10.0.1 gives 1. May 22 '15 at 13:52

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