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- ...ade School (Grades 3, 4, 5, 6, 7, 8 + Algebra 1) and High School (Regional and State Finals). ...abulated. The top 10 schools at each grade level will receive certificates and be recognized in the ICTM Bulletin.8 KB (1,182 words) - 13:26, 3 April 2024
- ...y of algebra involves familiarity with introductory topics to a high level and a multitude of new topics. ** [[Sum and difference of powers]]2 KB (198 words) - 15:06, 7 December 2024
- .... the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdots </math> and the sequence is <math>c_0, c_1, c_2,\ldots</math>. ...derived using the [[Geometric sequence#Infinite|sum formula for geometric series]] <cmath>\frac{1}{1-x} = \sum_{k=0}^{\infty} x^k = 1 + x + x^2 + x^3 + \do4 KB (659 words) - 11:54, 7 March 2022
- ...1, 3, 9, -27</math> and <math>-3, 1, 5, 9, \ldots</math> are not geometric sequences, as the ratio between consecutive terms varies. .../math>, <math>b</math>, and <math>c</math> are in geometric progression if and only if <math>b / a = c / b</math>.4 KB (649 words) - 20:09, 19 July 2024
- ...0, 7, 14</math> and <math>4, 12, 36, 108, \ldots</math> are not arithmetic sequences, as the difference between consecutive terms varies. ...math>, <math>b</math>, and <math>c</math> are in arithmetic progression if and only if <math>b - a = c - b</math>.4 KB (736 words) - 01:00, 7 March 2024
- .../math> can be written in the form <math>m/n</math> where <math>m_{}</math> and <math>n_{}</math> are relatively prime positive integers, find <math>m+n</m ...of <math>1</math> to <math>4</math> <tt>H</tt>'s separated by <tt>T</tt>'s and end with <math>5</math> <tt>H</tt>'s. Since the probability that the sequen7 KB (1,087 words) - 12:09, 17 November 2024
- ...e <math>m</math>, <math>n</math>, and <math>p</math> are positive integers and <math>m</math> is not divisible by the square of any prime. Find <math>100m ...es be <math>x</math>. Then, the common ratio is <math>\frac{1}{8x}</math>, and the first term is <math>8x^2</math>.4 KB (710 words) - 15:06, 2 June 2024
- ...math>g_n</math> are the <math>n</math>th terms of arithmetic and geometric sequences, respectively. ...</math>, where <math>d</math> is the common difference of <math>a_n</math> and <math>r</math> is the common ratio of <math>g_n</math>. Or, <math>\frac{a_n2 KB (477 words) - 18:39, 17 August 2020
- Find <math>a + b</math> if <math>a</math> and <math>b</math> satisfy <math>3a + 7b = 1977</math> and <math>5a + b = 2007</math>.30 KB (4,794 words) - 22:00, 8 May 2024
- ...and Wendy their oldest daughter. Tony is the youngest child. Twins Joshua and Alexis are <math>12</math> years old. Single-day passes cost <math>\textdollar{33}</math> for adults (Jerry and Hannah), <math>\textdollar{22}</math> for children71 KB (11,749 words) - 11:39, 20 November 2024
- ...The sum of the first series is <math>r_1</math>, and the sum of the second series is <math>r_2</math>. What is <math>r_1 + r_2</math>? ...t that the sums of the given two sequences are <math>\frac a{1-r_1}</math> and <math>\frac a{1-r_2}</math>.3 KB (453 words) - 09:22, 6 October 2023
- We can rigorously define <math>R[x]</math> to be the set of all sequences of elements of <math>R</math> with only finitely many terms nonzero: ...math>. We also do not care about the order in which the terms are written, and indeed often list them in descending order of power. So we would write:12 KB (2,010 words) - 23:10, 2 August 2020
- ...d throughout, and time is devoted to advanced topics like telescoping sums and piecewise functions. (Note: This class is equivalent to the second half of '''Week 2''': Completing the square and the quadratic formula1 KB (134 words) - 21:11, 17 January 2023
- ...re linearly dependent. Indeed, if we define <math>T = \lambda I - A</math> and let <math>\bold{T}^1, \bold{T}^2, \ldots, \bold{T}^n</math> denote the colu ...> such that <math>(\lambda I - A) \bold{v} = \bold{O}</math>. Distributing and re-arranging, <math>A\bold{v} = \lambda\bold{v}</math>, as desired. In the19 KB (3,412 words) - 13:57, 21 September 2022
- ...{1}{m^2}</math> <math>m-1</math> times, <math>\ldots</math>. To make other sequences, we can split <math>m-1</math> <math>\frac{1}{m^i}</math>s into <math>m(m-1 ...., x_{2011}</math> are nonnegative integers. We plug in <math>m = 1</math> and see that <cmath>P(1) = 1 - 1 - 1... -1 = 1-2011 = -2010</cmath> Now, we can11 KB (1,811 words) - 19:45, 1 September 2024
- ...a second sequence of terms by subtracting each term by the following term and taking it modulus 3, i.e. (1-0, 0-1, 1-0, 0-1, ... 0-1, 1-0, 0-2, 2-1) = 12 ...s left is simply the "negative" of the term generated by the changing side and the side to its right (i.e. 212 to 202 changes 12 to 21).2 KB (355 words) - 04:48, 18 April 2018
- ...f the eleventh term of the first series to the eleventh term of the second series is: ...</math>, so the common difference of <math>S</math> is <math>3b-16a</math> and the common difference of <math>T</math> is <math>7b-62a</math>.3 KB (572 words) - 22:44, 3 April 2023
- Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a f ...getting all heads. Then the next probability is all of them getting tails and then on the second try, they all get heads. The probability of that happeni2 KB (338 words) - 00:32, 10 November 2024
- ...BC. AP Calculus AB is supposed to be roughly equal to the first semester and a half of a typical year-long introductory, single-variable college calculu **Trigonometric, logarithmic, and exponential limits5 KB (665 words) - 14:27, 3 March 2016
- ...h day thereafter Anh read one more page than she read on the previous day, and it took her one more minute than on the previous day until she completely r ...19</math>, and <math>374</math>. The only such numbers are <math>1</math> and <math>11</math>. We know that Anh reads for at least <math>2</math> days.5 KB (818 words) - 00:25, 10 January 2024