A Fibonacci Series Problem

Описание к видео A Fibonacci Series Problem

We evaluate the sum from 1 to infinity of F_n^2/3^n, where F_n is the nth Fibonacci number.

Showing the original series is convergent:
Use Binet's formula to write F_n = (ϕ^n - ϕ^{-1})/sqrt{5}, then apply the comparison test with e.g. (ϕ^2 / 3)^n.

Shortcut way of dealing with T, the second sum:
https://proofwiki.org/wiki/Cassini%27...

00:00 Intro
00:32 Writing the sum in terms of itself
05:39 Dealing with the remaining sum
11:53 Convergence

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