How to Solve the Golden Limit Challenge

In this video we solve what we call the "Golden Limit Challenge". We first start by figuring out how the sequence operates. We then show that it is the ratio between the Fibonacci's sequence n-th term and the next term. So we can easily compute the underlying problem using the telescopic method. Computing the limit becomes therefore straightforward.

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[sachapaykin]

A more systematic proof would be to take the log of (a_1*...*a_(n-1))^1/n and use Cesaro's theorem, after noticing that a_n -> 1/phi when n->inf

[SuperYoonHo]

Oh wow never suspected that fibonacci numbers would sneak up in this video:)

[john-hermannbignon]

In all honesty, I have been totally blown away when I saw that you were recording videos in English...you speak with such confidence...👏👏👏👏👏👏 This just speaks volume about the great vision that you have for this channel...I respectfully salute this endeavor of yours brother...May this go all the way by the grace of God! 🙏🙏🙏🙏🙏