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 on this page are the property of the MAA's American Mathematics Competitions