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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- Jul 2nd 2007, 06:31 AMgalactusanother fibonacci infinite sum
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 = - Jul 6th 2007, 06:38 AMgalactus
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