Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 17"
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== Problem == | == Problem == | ||
+ | Let <math>[x]</math> represent the greatest integer that is less than or equal to <math>x</math>. For example, <math>[2.769]=2</math> and <math>[\pi]=3</math>. Then what is the value of | ||
− | <center><math> \mathrm{(A) \ } \qquad \mathrm{(B) \ } \qquad \mathrm{(C) \ } \qquad \mathrm{(D) \ } \qquad \mathrm{(E) \ } </math></center> | + | <center><math> [\log_2 2] + [\log_2 3] + [\log_2 4] + \cdots + [\log_2 99] + [\log_2 100] ?</math></center> |
+ | |||
+ | <center><math> \mathrm{(A) \ } 480 \qquad \mathrm{(B) \ }481 \qquad \mathrm{(C) \ }482 \qquad \mathrm{(D) \ }483 \qquad \mathrm{(E) \ }484 </math></center> | ||
== Solution == | == Solution == | ||
+ | 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>. | ||
== See also == | == See also == | ||
* [[University of South Carolina High School Math Contest/1993 Exam]] | * [[University of South Carolina High School Math Contest/1993 Exam]] |
Revision as of 20:15, 22 July 2006
Problem
Let represent the greatest integer that is less than or equal to . For example, and . Then what is the value of
Solution
The sum reduces to .