iccanobiF Sequence

Number Theory Level 2

Starting with $F_1 = 1$ , $F_2 = 1$ and then performing $F_n = F_{n-1} + F_{n-2}$ , we get the sequence of Fibonacci Numbers , $F_n$ . However, we can also extend this backwards, and look at when $n < 1$ .

Using this, what is the value of $F_{2018} + F_{-2018}$ ?

The answer is 0.

1 solution

Jacopo Piccione
Jun 21, 2018

First we notice that $F_{-x} = \begin{cases} \ F_{x} & \text{if x is odd } \\ - F_{x} & \text{if x is even } \end{cases}$ with $x>0$ Since 2018 is even, $F_{-2018}+F_{2018}=-F_{2018}+F_{2018}=0$

iccanobiF Sequence

The answer is 0.

1 solution

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