Soroban, here's another fun fibonacci sum for ya'. Prove that: 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: Now, So it's left to show that . Because Based on the observation that = the Fibonacci sequence, and Let , then and Then we get: But So, we are left with And we have
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