A Fibonacci Sum.
<p>The Fibonacci sequence is arguably one of the most known sequences in the world, as well as most studied. To the unfamiliar, it is the sequence whose elements are the sum of the previous two. We can denote this by writing F_n = F_(n-1) + F_(n-2) where F_0 = 0, F_1 = 1 and so on. Now the question is, how can we find this sum, which traces out the digits of the Fibonacci sequence in the numerator. This is what we look at in this article.</p>
<p>Firstly, let us focus on the recurrence relation itself. We have the following, to begin with:</p>
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