Problem:
The symbolism βxβ denotes the largest integer not exceeding x. For example, β3β=3, and β9/2β=4. Compute
β1ββ+β2ββ+β3ββ+β―+β16ββ.
Answer Choices:
A. 35
B. 38
C. 40
D. 42
E. 136
Solution:
The first three values in the sum are 1, the next five are 2, the next seven are 3, and the final one is 4 for a total of
3β
1+5β
2+7β
3+1β
4=38.
Answer: Bβ.
The problems on this page are the property of the MAA's American Mathematics Competitions