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- The '''American Mathematics Competitions''' (AMC) consist of a series of increasingly difficult tests for students in middle school and high scho * [[American Invitational Mathematics Examination]] (AIME) — high scorers from the AMC 10/12 exams.5 KB (696 words) - 02:47, 24 December 2019
- * Performance on AMC and AIME, including current and previous years. *[[AMC]] and [[AIME]] performance22 KB (3,532 words) - 10:25, 27 September 2024
- ...heavily on developing deep understanding of the methods of [[mathematical problem solving]]. [https://artofproblemsolving.com/school/handbook/prospective/ab * [[Math Jams]] are free classes that include information sessions, problem solving lessons, and competition solution discussion immediately after majo8 KB (965 words) - 02:41, 17 September 2020
- ...power of <math>p</math> in the prime factorization of <math>n!</math>. The series is formally infinite, but the terms converge to <math>0</math> rapidly, as <math>\mathrm{(A)}\,0\quad\mathrm{(B)}\,1\quad\mathrm{(C)}\,3\quad\mathrm{(D)}\,5\quad\mathrm{(E)}\,7\quad\mathr10 KB (809 words) - 15:40, 17 March 2024
- ...ath>c</math> are in geometric progression if and only if <math>b / a = c / b</math>. A '''geometric series''' is the sum of all the terms of a geometric sequence. They come in two va4 KB (649 words) - 20:09, 19 July 2024
- ...th>c</math> are in arithmetic progression if and only if <math>b - a = c - b</math>. ...arithmetic sequence. All infinite arithmetic series diverge. As for finite series, there are two primary formulas used to compute their value.4 KB (736 words) - 01:00, 7 March 2024
- == Problem == ...ount of <math>96 + 91 + 86 + \ldots + 1</math>. Summing this [[arithmetic series]] of <math>20</math> terms, we get <math>970</math>. However, we have negl2 KB (353 words) - 21:56, 27 September 2024
- == Problem == ...times the sum of the original series. The common [[ratio]] of the original series is <math> \frac mn </math> where <math> m </math> and <math> n </math> are3 KB (581 words) - 20:19, 22 September 2024
- {{AIME Problems|year=2005|n=II}} == Problem 1 ==7 KB (1,119 words) - 20:12, 28 February 2020
- == Problem == ...</math>, <math>a_{m-1}a_{m-2} = 3</math>; from the recursion given in the problem <math>a_{m-p+1} = a_{m-p-1} - 3/a_{m-p}</math>, so <math>a_{m-p+1} = 3p/a_{3 KB (499 words) - 17:52, 21 November 2022
- == Problem == ...ctly, but there is one obvious transformation to make: sum the [[geometric series]]:2 KB (298 words) - 19:02, 4 July 2013
- == Problem == Graphing this yields a series of [[rectangle]]s which become smaller as you move toward the [[origin]]. T2 KB (303 words) - 17:43, 16 October 2024
- {{AIME Problems|year=1989}} == Problem 1 ==7 KB (1,045 words) - 00:18, 5 January 2025
- {{AIME Problems|year=2002|n=II}} == Problem 1 ==7 KB (1,177 words) - 14:42, 11 August 2023
- == Problem == Using the [[geometric series]] formula, <math>1 - x + x^2 + \cdots - x^{17} = \frac {1 - x^{18}}{1 + x}6 KB (872 words) - 15:51, 9 June 2023
- == Problem == ...thereby represent <math>S</math> as the sum of <math>n-1</math> arithmetic series of <math>1000, 999, \ldots, 1001 - \left\lfloor \frac{121-n}{n-1} \right\rf5 KB (851 words) - 17:01, 28 December 2022
- == Problem == ...math>, one obtains the squares of three consecutive terms of an arithmetic series. Find <math>k</math>.2 KB (320 words) - 14:50, 12 September 2024
- == Problem == ...nteger]]s such that <math>b+c+d</math> is a [[perfect square]] and <math>a+b+c+d+e</math> is a [[perfect cube]], what is the smallest possible value of3 KB (552 words) - 11:41, 3 March 2024
- == Problem == .... To figure out which rational number, we sum an [[infinite]] [[geometric series]], <math>0.d25d25d25\ldots = \sum_{n = 1}^\infty \frac{d25}{1000^n} = \frac4 KB (584 words) - 13:38, 11 August 2024
- == Problem == ...168 congruent segments with points <math>C_{}^{}=Q_0, Q_1, \ldots, Q_{168}=B</math>. For <math>1_{}^{} \le k \le 167</math>, draw the segments <math>\ov4 KB (595 words) - 11:51, 17 June 2021