Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 17"
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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>. | 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>. | ||
| − | + | ---- | |
| − | * [[University of South Carolina High School Math Contest/1993 Exam]] | + | |
| + | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 16|Previous Problem]] | ||
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| + | [[Category:Intermediate Algebra Problems]] | ||
Revision as of 12:16, 23 July 2006
Problem
Let ![$[x]$](http://latex.artofproblemsolving.com/b/c/e/bceb7b14e55d33a8bca29b7863ad3cdae95afce4.png)
represent the greatest integer that is less than or equal to 
. For example, ![$[2.769]=2$](http://latex.artofproblemsolving.com/e/a/0/ea00c60462a76b3a9d1bd31fafcf4a74c14c1952.png)
and ![$[\pi]=3$](http://latex.artofproblemsolving.com/e/c/a/eca8ceb8df76099894c58849611d9b55c84c9389.png)
. Then what is the value of
![$[\log_2 2] + [\log_2 3] + [\log_2 4] + \cdots + [\log_2 99] + [\log_2 100] ?$](http://latex.artofproblemsolving.com/8/9/1/8911a07bc67d61a830386e643a7e75b2c80c2d57.png)
Solution
The sum reduces to 
.
