Why is the convergent product with GoldenRatio evaluated as ComplexInfinity?

It is true that the following product has a singularity for k = 1, but from k = 2 it is convergent.
We can be convinced of this by numerical calculation:

 N[Product[1/(1 - 1/GoldenRatio^k*(1 + k/GoldenRatio)), {k, 2, 1000}], 60]
 N[Product[1/(1 - 1/GoldenRatio^k*(1 + k/GoldenRatio)), {k, 2, 2000}], 60]

(* 167.566103786067378643031697535002496062682533360948646334201
   167.566103786067378643031697535002496062682533360948646334201 *)

But I discovered a bug if the product starts from 2.

 Product[1/(1 - 1/GoldenRatio^k*(1 + k/GoldenRatio)), {k, 2, Infinity}]

 (* Power::infy: Infinite expression 1/0 encountered.
 ComplexInfinity *)

Why is evaluated as ComplexInfinity ?