mcc wrote: ↑Sat Dec 29, 2018 8:38 am

And it is said, that

this sum tends to the reciprocal of the golden ratio

That's a great example of how you can completely destroy the meaning of a phrase by taking it out of context. Here's the complete paragraph in question, copied and pasted from the English Wikipedia:

The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. Since this is less than 1, the ratio test shows that the sum converges.

What tends to the reciprocal of the golden ratio is

the ratio of successive terms, not the sum of the series. Since each term is the reciprocal of an element of the Fibonacci series, and since the ratio of successive elements of the Fibonacci series is known to tend to the golden ratio, this is a rather trivial observation. The point of the observation is that the

ratio test applies, and proves that the sum of the series converges.