Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 17"
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− | + | <math>[\log_2 n]</math> is the largest [[integer]] <math>m</math> such that <math>2^m \leq n</math>. If we grouping the terms of our sum according to their value of <math>m</math>, the sum reduces to <math>2(1)+4(2)+8(3)+16(4)+32(5)+37(6)=2+8+24+64+160+222=480</math>. | |
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Revision as of 12:17, 1 August 2006
Problem
Let represent the greatest integer that is less than or equal to . For example, and . Then what is the value of
Solution
is the largest integer such that . If we grouping the terms of our sum according to their value of , the sum reduces to .