Please help with this general formula/sum of sequence question

I think this is the golden ratio (sqrt(5) + 1) / 2 represented as "continued fraction" as follows:

1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/a(n)))))))))))))))))))))))=Sqrt(5).