Search results
Create the page "2005 AIME II Problem 1" on this wiki! See also the search results found.
Page title matches
- == Problem == ...given by the [[binomial coefficient]] <math>{n \choose 6} = \frac{n\cdot(n-1)\cdot(n-2)\cdot(n-3)\cdot(n-4)\cdot(n-5)}{6\cdot5\cdot4\cdot3\cdot2\cdot1}<1 KB (239 words) - 11:54, 31 July 2023
Page text matches
- ...d only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. ==== Problem ====9 KB (1,703 words) - 01:20, 7 December 2024
- * <math>\binom{n-1}{r-1}+\binom{n-1}{r}=\binom{n}{r}</math> * <math>\binom{n}{r}=\frac{n}{r}\binom{n-1}{r-1}</math>4 KB (638 words) - 21:55, 5 January 2025
- MC(90,"\mbox{semiminor axis}",7,D((0,0)--(0,3),green+linewidth(1)),E); MC("\mbox{semimajor axis}",7,D((0,0)--(5,0),red+linewidth(1)),S);5 KB (892 words) - 21:52, 1 May 2021
- ...numbers''' arise when we try to solve [[equation]]s such as <math> x^2 = -1 </math>. ...this addition, we are not only able to find the solutions of <math> x^2 = -1 </math> but we can now find ''all'' solutions to ''every'' polynomial. (Se5 KB (860 words) - 15:36, 10 December 2023
- ...ratio <math>-1/2</math>; however, <math>1, 3, 9, -27</math> and <math>-3, 1, 5, 9, \ldots</math> are not geometric sequences, as the ratio between cons ...ogression if and only if <math>a_2 / a_1 = a_3 / a_2 = \cdots = a_n / a_{n-1}</math>. A similar definition holds for infinite geometric sequences. It ap4 KB (649 words) - 21:09, 19 July 2024
- ...there will always be an infinite number of solutions when <math>\gcd(a,b)=1</math>. If <math>\gcd(a,b)\nmid c</math>, then there are no solutions to t .../math> is an [[odd]] number, then <math>m, \frac {m^2 -1}{2}, \frac {m^2 + 1}{2}</math> is a Pythagorean triple.9 KB (1,434 words) - 01:15, 4 July 2024
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME II Problems]]1 KB (135 words) - 12:24, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME I Problems]]1 KB (154 words) - 12:30, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AIME I Problems]]1 KB (135 words) - 12:31, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME II Problems]]1 KB (135 words) - 12:30, 22 March 2011
- {{AIME Problems|year=2006|n=I}} == Problem 1 ==7 KB (1,173 words) - 03:31, 4 January 2023
- == Problem == ...given by the [[binomial coefficient]] <math>{n \choose 6} = \frac{n\cdot(n-1)\cdot(n-2)\cdot(n-3)\cdot(n-4)\cdot(n-5)}{6\cdot5\cdot4\cdot3\cdot2\cdot1}<1 KB (239 words) - 11:54, 31 July 2023
- == Problem == === Solution 1 ===4 KB (628 words) - 11:28, 14 April 2024
- == Problem == An [[infinite]] [[geometric series]] has sum 2005. A new series, obtained by squaring each term of the original series, has 13 KB (581 words) - 21:19, 22 September 2024
- == Problem == == Solution 1 ==3 KB (377 words) - 18:36, 1 January 2024
- == Problem == ...egers <math>\frac{10}{a}</math> has to be an integer, so <math>a=1,2,5,10,-1,-2,-5,-10</math>. Thus the product of the roots is equal to one of the foll4 KB (642 words) - 02:14, 1 June 2024
- == Problem == ...og_a b + 6\log_b a=5, 2 \leq a \leq 2005, </math> and <math> 2 \leq b \leq 2005. </math>3 KB (547 words) - 19:15, 4 April 2024
- == Problem == ...<math> (n+1) </math> becomes the bottom card of the new stack, card number 1 is on top of this card, and so on, until piles <math> A </math> and <math>2 KB (384 words) - 00:31, 26 July 2018
- {{AIME Problems|year=2005|n=II}} == Problem 1 ==7 KB (1,119 words) - 21:12, 28 February 2020
- == Problem == ...}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}. </math> Find <math>(x+1)^{48}</math>.2 KB (279 words) - 12:33, 27 October 2019
