Fibonacci Numbers
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: \(1, 1, 2, 3, 5, 8, 13, ... \)
by
Abdulrahman El Shafei
Find the last digit of the 123456789-th Fibonacci number.
by
Danish Ahmed
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?
by
Sam Thompson
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 \(F_{2013}\).
by
Calvin Lin
\[\sum_{n=0}^{\infty} \frac{F_{n}}{3^{n}}= \ ? \]
Details and Assumptions
\(F_{n}\) is the \(n^\text{th} \) Fibonacci number, with \(F_{1} = F_{2} = 1\).
by
Joel Yip