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- ...mation that one can have about a polynomial of one variable is the highest power of the variable which appears in the polynomial. This number is known as t * [[Newton sums]]6 KB (1,100 words) - 14:57, 30 August 2024
- ...cient way of finding the sums of [[root]]s of a [[polynomial]] raised to a power. They can also be used to derive several [[factoring]] [[identity|identiti Newton's sums tell us that,4 KB (704 words) - 07:28, 24 November 2024
- ==Power Sets== {{main|power set}}11 KB (2,019 words) - 16:20, 7 July 2024
- ...Each of three players randomly selects and keeps three of the tiles, and sums those three values. The [[probability]] that all three players obtain an [ ...th>i^2 = - 1.</math> Let <math>S_n</math> be the sum of the complex power sums of all nonempty [[subset]]s of <math>\{1,2,\ldots,n\}.</math> Given that <7 KB (1,084 words) - 01:01, 28 November 2023
- ...s of all those positive [[integer]]s which are [[exponent|powers]] of 3 or sums of distinct powers of 3. Find the <math>100^{\mbox{th}}</math> term of this Rewrite all of the terms in base 3. Since the numbers are sums of ''distinct'' powers of 3, in base 3 each number is a sequence of 1s and5 KB (866 words) - 23:00, 21 December 2022
- ...th>i^2 = - 1.</math> Let <math>S_n</math> be the sum of the complex power sums of all nonempty [[subset]]s of <math>\{1,2,\ldots,n\}.</math> Given that < ...(for now, including the empty subset, which we will just define to have a power sum of zero) with <math>9</math> in it is equal to the number of subsets wi2 KB (385 words) - 15:47, 14 September 2024
- ...1)\sqrt{n} }{k^n - 1} </math>. But since there are <math>k^n </math> such sums, by the [[pigeonhole principle]], two must fall into the same subinterval.2 KB (349 words) - 03:36, 28 May 2023
- ...ree''' of a [[polynomial]] in one [[variable]] is the largest [[exponent | power]] with which the variable appears with non-zero [[coefficient]]. Thus, for ...he exponents of the variables in each term and taking the largest of these sums. For example, the polynomial <math>Q(x, y, z) = x^2yz + 2xz^3 + y^4z^2</ma1 KB (203 words) - 18:38, 30 January 2007
- ..._3\zeta_1,\ e_3 = \zeta_1\zeta_2\zeta_3</math> (the [[elementary symmetric sums]]). Then, we can rewrite the above equations as Let <math>s_n = \zeta_1^n + \zeta_2^n + \zeta_3^n</math> (the [[power sums]]). Then from <math>(1)</math>, we have the [[recursion]] <math>s_{n+3} = s2 KB (221 words) - 01:49, 19 March 2015
- far above our poor power to add or detract. The world will little note nor long dead who struggled here have hallowed it far above our poor power to add or29 KB (4,929 words) - 12:26, 12 September 2024
- ...mial Theorem, we raise both sides of <math>a+a^{-1}=4</math> to the fourth power: <li>To find the fourth power of a sum/difference, we can first square that sum/difference, then square t4 KB (663 words) - 06:32, 4 November 2022
- Also, Newton's Sums yields an answer through the application. ...> and <math>(t+r)</math> are roots of this polynomial, we know that (using power reduction)7 KB (1,251 words) - 18:18, 2 January 2024
- ...e people will have reasonably inexpensive options for switching to cleaner power sources. Even now most families could switch to biomass for between <math>\ ...ts thinking about cubes and computes some sums of cubes, and some cubes of sums:71 KB (11,749 words) - 11:39, 20 November 2024
- ...ath> with coefficients in <math>R</math>." That is, it is the ring of all sums of the form ...h 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
- ...h <math>a+b+c+d+e=2010</math> and let <math>M</math> be the largest of the sums <math>a+b</math>, <math>b+c</math>, <math>c+d</math> and <math>d+e</math>. ...integer <math>n\ge2</math>, let <math>\text{pow}(n)</math> be the largest power of the largest prime that divides <math>n</math>. For example <math>\text{p12 KB (1,845 words) - 12:00, 19 February 2020
- Exponentiating this matrix to the <math>n</math>th power will yield [[binomial coefficient]]s as follows A note about this argument: all of the power series used here are defined formally, and so we do not actually need to wo19 KB (3,412 words) - 13:57, 21 September 2022
- ...the <math>2^{5}</math> possible coefficients is multiplied by a different power of <math>x</math> because there are also <math>2^5</math> different powers ...h>E</math> be the point of tangency of the circle with <math>AC</math>. By power of a point, <math>CD \cdot CB = CE^2</math>, that is, <math>9 \cdot 25 = C^36 KB (6,214 words) - 19:22, 13 July 2023
- ...r, by Vieta's formulas, we know that <math>P_1=2</math>. Also, by Newton's Sums, as the coefficients of <math>x^{n-k}</math> for <math>k=2,3,\dots,32</math The <math>32</math>nd power of each of these roots is just <math>1</math>, hence the sum of the <math>38 KB (1,348 words) - 08:44, 25 June 2022
- ...h>, where <math>\textrm{pow}_{\textrm{larg}}</math> represents the largest power of <math>2</math> that is smaller than <math>n</math>. I will call this sum ...Already it looks like <math>f(n)</math> is only odd if <math>n=2^{\textrm{power}}-1</math>.6 KB (1,069 words) - 13:05, 28 November 2022
- The diagram shows a magic square in which the sums of the numbers in any row, column or diagonal are equal. What is the value ...in zero. The product of any pair, <math>p</math> and <math>q,</math> is a power of 10 (that is, 10, 100, 1000, 10 000 , ...). If <math>p > q</math> , the l10 KB (1,590 words) - 15:43, 29 January 2021