Problem:
What is the value of
(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)?
Answer Choices:
A. 70
B. 97
C. 127
D. 159
E. 729
Solution:
======​(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)(2(2(2(2(2(3)+1)+1)+1)+1)+1)(2(2(2(2(7)+1)+1)+1)+1)(2(2(2(15)+1)+1)+1)(2(2(31)+1)+1)(2(63)+1)(C)127​​
Observe that each intermediate result is 1 less than a power of 2.
The problems on this page are the property of the MAA's American Mathematics Competitions