Discrete Mathematics
# Fibonacci Numbers

Find the last digit of the 123456789-th Fibonacci number.

In the Fibonacci sequence, $F_{0}=1$, ${F_1}=1$, and for all $N>1$, $F_N=F_{N-1}+F_{N-2}$.

How many of the first 2014 Fibonacci terms end in 0?

The Fibonacci sequence is defined by $F_1 = 1, F_2 = 1$ and $F_{n+2} = F_{n+1} + F_{n}$ for $n \geq 1$.

Find the greatest common divisor of $F_{484}$ and $F_{2013}$.

$\sum_{n=0}^{\infty} \frac{F_{n}}{3^{n}}= \ ?$

**Details and Assumptions**

$F_{n}$ is the $n^\text{th}$ Fibonacci number, with $F_{1} = F_{2} = 1$.