Problem:
For all integers n greater than 1 , define an​=logn​20021​. Let b=a2​+a3​+a4​+a5​ and c=a10​+a11​+a12​+a13​+a14​. Then b−c equals
Answer Choices:
A. −2
B. −1
C. 20021​
D. 10011​
E. 21​
Solution:
We have an​=logn​20021​=log2002​n, so
b−c=(log2002​2+log2002​3+log2002​4+log2002​5)−(log2002​10+log2002​11+log2002​12+log2002​13+log2002​14)=log2002​10⋅11⋅12⋅13⋅142⋅3⋅4⋅5​=log2002​11⋅13⋅141​=log2002​20021​=−1​​
The problems on this page are the property of the MAA's American Mathematics Competitions