High School Math Contest University of South Carolina December 8, 2007
... 10. The king took a cup filled with water and drank 1/5 of its contents. When the king looked away, the court jester refilled the cup by adding alcohol to the remaining water and then stirred. The king drank 1/4 of this liquid mixture. When the king looked away again, the court jester refilled the c ...
... 10. The king took a cup filled with water and drank 1/5 of its contents. When the king looked away, the court jester refilled the cup by adding alcohol to the remaining water and then stirred. The king drank 1/4 of this liquid mixture. When the king looked away again, the court jester refilled the c ...
Worksheet I: What is a proof (And what is not a proof)
... A paradox also known as the surprise examination paradox or prediction paradox. A prisoner is told that he will be hanged on some day between Monday and Friday, but that he will not know on which day the hanging will occur before it happens. He cannot be hanged on Friday, because if he were still al ...
... A paradox also known as the surprise examination paradox or prediction paradox. A prisoner is told that he will be hanged on some day between Monday and Friday, but that he will not know on which day the hanging will occur before it happens. He cannot be hanged on Friday, because if he were still al ...
BALANCING WITH FIBONACCI POWERS 1. Introduction As usual {F
... Then for all integers u ≥ u0 , αu+δ2 ≤ Fu ≤ αu+δ1 . In order to make the application of Lemma 2.2 more convenient, we take u0 ≥ 6 and get the following result. Corollary 2.3. If u0 ≥ 6, then δ1 < −1.66 and δ2 > −1.68. The following result, which is Lemma 6 in [3], gives upper bounds for linear combi ...
... Then for all integers u ≥ u0 , αu+δ2 ≤ Fu ≤ αu+δ1 . In order to make the application of Lemma 2.2 more convenient, we take u0 ≥ 6 and get the following result. Corollary 2.3. If u0 ≥ 6, then δ1 < −1.66 and δ2 > −1.68. The following result, which is Lemma 6 in [3], gives upper bounds for linear combi ...
1 Sequences, Series, how to decide if a series in convergent
... will converge to the same limit regardless of how they are re-ordered. This statement is part of the section called absolute convergence if you look up series in a textbook. We need simple ways to decide whether series converge or diverge. Lets restrict our attention to series where all terms are t ...
... will converge to the same limit regardless of how they are re-ordered. This statement is part of the section called absolute convergence if you look up series in a textbook. We need simple ways to decide whether series converge or diverge. Lets restrict our attention to series where all terms are t ...
