Fibonacci Numbers: Level 3 Challenges Practice Problems Online

Compute $\frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \dots + \frac{F_k}{2^k} + \dots$ where $F_k$ represents the the $k^\text{th}$ term of the Fibonacci sequence: $1, 1, 2, 3, 5, 8, 13, ...$

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 $F_{1} = F_{2} = 1$ .

Fibonacci Numbers

Challenge Quizzes

Fibonacci Numbers: Level 3 Challenges