Soroban, here's another fun fibonacci sum for ya'.
In other words, prove:
As you probably know, is the golden ratio.
golden ratio =
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Rather anyone cares or not, but here is how I tackled this.
I started with:
So it's left to show that .
Based on the observation that = the Fibonacci sequence, and
Let , then
Then we get:
So, we are left with
And we have
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