Exercise 5.

The Fibonacci sequence is \(0, 1, 1, 2, 3, 5, 8, 13, \ldots\) (where \(F_0 = 0\)).

  1. Write out the first few terms of the sequence of partial sums: \(0\text{,}\) \(0+1\text{,}\) \(0+1+1\text{,}\)

  2. Guess a formula for the sequence of partial sums expressed in terms of a single Fibonacci number. For example, you might say \(F_0 + F_1 + \cdots + F_n = 3F_{n-1}^2 + n\text{,}\) although that is definitely not correct.

Solution.
in-context