Roger,

Ok, the formula produces garbage for very small k...
any fibonacci number smaller than 10^10.  It also
doesnt include the last binet term that is only useful
for determining small fibonacci numbers.

Anyways, unrelated to original question:
This seems like a real precision bug though...

    102j100 ": x:(%: 2)
1.4142135623731390970412181031989721904863670411925480575736180767789366814500092718645843712378263880

amount cut off to match below:
1.4142135623731390970412181031989
windows calculator: for sqrt 2
1.4142135623730950488016887242097

the 2 numbers diverge around decimal position 12


        

        
                
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