Question 4
The Fibonacci numbers are
$$F_1=1,\quad F_2=1,\quad F_3=2,\quad F_4=3,\quad F_5=5,\quad F_6=8,\quad F_7=13,\ldots$$
The first two are both 1, and each later number is the sum of the two preceding it. What is the last digit of the sum of the first 2005 Fibonacci numbers?
$$F_1=1,\quad F_2=1,\quad F_3=2,\quad F_4=3,\quad F_5=5,\quad F_6=8,\quad F_7=13,\ldots$$
The first two are both 1, and each later number is the sum of the two preceding it. What is the last digit of the sum of the first 2005 Fibonacci numbers?