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I am suprised that mathematica is not able to find the function for the following sequence:

FindSequenceFunction[{1/Sqrt[2], 1/Sqrt[3], 1/Sqrt[4], 
                      1/Sqrt[5], 1/Sqrt[6], 1/Sqrt[7], 1/Sqrt[8]}]

But if I square it, it doesn't have any problems finding the solution:

FindSequenceFunction[{1/Sqrt[2], 1/Sqrt[3], 1/Sqrt[4], 1/Sqrt[5], 
                      1/Sqrt[6], 1/Sqrt[7], 1/Sqrt[8]}^2]

Have you any idea why it behaves that strange?

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    $\begingroup$ You are allowed to help Mathematica: FindSequenceFunction[{1/Sqrt[2], 1/Sqrt[3], 1/Sqrt[4], 1/Sqrt[5], 1/Sqrt[6], 1/Sqrt[7], 1/Sqrt[8]}^2, n]^(1/2) (assuming n>=0) $\endgroup$ – Bob Hanlon Mar 1 '18 at 0:43
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If you examine the documentation page of FindSequenceFunction you'll see it has an option called FunctionSpace. Its doc page makes clear that the type of function that would match this sequence is not available.

Possible values are "Polynomial", "RationalFunction", "HypergeometricTerm", "ConstantRecursive", "HolonomicSequence" as continuous function spaces and "Polynomial", "RationalFunction","Hypergeometric", "HolonomicFunction" as discrete function spaces.

1/Sqrt[n] does not belong to any of these spaces.

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