A Fibonacci Series Problem
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YouTubeDr Barker
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's_Identity ...
5.4K viewsSep 13, 2024
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