Problem:
What is the value of the product
(1+11​).(1+21​).(1+31​).(1+41​).(1+51​).(1+61​)?
Answer Choices:
A. 67​
B. 34​
C. 27​
D. 7
E. 8
Solution:
Let's first note that if we are given an expression of the form 1+n1​ we can rewrite this as
nn​+n1​=nn+1​.
With that in mind, we can rewrite the expression given to us in the problem, as shown below:
​(1+11​)⋅(1+21​)⋅(1+31​)⋅(1+41​)⋅(1+51​)⋅(1+61​)=12​⋅23​⋅34​⋅45​⋅56​⋅67​=7​
Thus, the correct answer is D.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions