Problem:
What is the value of
(((2+1)−1+1)−1+1)−1+1?
Answer Choices:
A. 85
B. 711
C. 58
D. 1118
E. 815
Solution:
Computing inside to outside yields:
(((2+1)−1+1)−1+1)−1+1=((34)−1+1)−1+1=(47)−1+1=(B)711.
Note: The successive denominators and numerators of numbers obtained from this pattern are the Lucas numbers.
The problems and solutions on this page are the property of the MAA's American Mathematics Competitions