1986 AHSME Problems/Problem 25
Problem
If is the greatest integer less than or equal to , then
Solution
Because , we have . We count how many times attains a certain value.
For all except for , we have that is satisfied by all , for a total of values of . If , can only have one value (). Thus, the desired sum looks like
Let be the desired sum without the . Multiplying by gives Subtracting the two equations gives Summing the geometric sequence in parentheses and simplifying, we get Finally, adding back the gives the desired answer
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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