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