Problem:
The symbolism ⌊x⌋ denotes the largest integer not exceeding x. For example, ⌊3⌋=3, and ⌊9/2⌋=4. Compute
⌊1​⌋+⌊2​⌋+⌊3​⌋+⋯+⌊16​⌋.
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
3â‹…1+5â‹…2+7â‹…3+1â‹…4=38.
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions