MathDB

3

Part of 2005 Chile National Olympiad

Problems(1)

max n such that Fibonacci number f_N<f_1+f_2+...+f_{2004}+f_{2005}

Source: Chile Finals 2005 L2 p3

10/3/2022
The Fibonacci numbers fnf_n are defined for each natural number nn as follows: f0=f1=1f_0=f_1=1 and for nn greater than or equal to 22, by recurrence: fn=fn−1+fn−2f_n=f_{n-1}+f_{n-2} Let S=f1+f2+...+f2004+f2005S=f_1+f_2+...+f_{2004}+f_{2005}. Calculate the largest value of NN, such that the Fibonacci number fNf_N satisfies fN<Sf_N<S
fibonacci numbernumber theory