Problem:
Let x1=97, and for n>1 let xn=xn−1n. Calculate the product x1x2⋯x8.
Solution:
For each n>1,xn−1xn=n. Using this fact for n=2,4,6 and 8, one obtains x1x2⋯x8=(x1x2)(x3x4)(x5x6)(x7x8)=2⋅4⋅6⋅8=384.
Note: Except for the fact that it must be nonzero, the value of x, does not affect the solution.
The problems on this page are the property of the MAA's American Mathematics Competitions