Number Sums - TI Education
... Texas Instruments 2014. You may copy, communicate and modify this material for non-commercial educational purposes provided all acknowledgements associated with this material are maintained. ...
... Texas Instruments 2014. You may copy, communicate and modify this material for non-commercial educational purposes provided all acknowledgements associated with this material are maintained. ...
AoPS Kings - Art of Problem Solving
... 22. A covenant armada of 15 dropships wants to organize itself in a set of 3 rectangular formations before going to battle. If each formation must have at least one dropship, how many ways can the armada go to battle? A 1 × 4 is different from a 2 × 2 but not different from a ...
... 22. A covenant armada of 15 dropships wants to organize itself in a set of 3 rectangular formations before going to battle. If each formation must have at least one dropship, how many ways can the armada go to battle? A 1 × 4 is different from a 2 × 2 but not different from a ...
Quantitative Ability – POINTS TO REMEMBER If an equation (i.e. f(x
... 17. a4 + b4 + c4 + d4 >= 4abcd (Equality arises when a=b=c=d=1) 18. (n!)2 > nn 19. If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s 20. If n is even, n(n+1)(n+2) is divisible by 24 21. x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) . ...
... 17. a4 + b4 + c4 + d4 >= 4abcd (Equality arises when a=b=c=d=1) 18. (n!)2 > nn 19. If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s 20. If n is even, n(n+1)(n+2) is divisible by 24 21. x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) . ...
Document
... The first and last coefficients are 1. The coefficients of the second and second to last terms are equal to n. Example: What are the last 2 terms of (x + y)10 ? Since n = 10, the last two terms are 10xy9 + 1y10. The coefficient of xn–ryr in the expansion of (x + y)n is written n or nCr . So, t ...
... The first and last coefficients are 1. The coefficients of the second and second to last terms are equal to n. Example: What are the last 2 terms of (x + y)10 ? Since n = 10, the last two terms are 10xy9 + 1y10. The coefficient of xn–ryr in the expansion of (x + y)n is written n or nCr . So, t ...
Pascal`s Triangle
... and find an explanation for it similar in style to our argument for the Pascal’s addition rule. ...
... and find an explanation for it similar in style to our argument for the Pascal’s addition rule. ...
Quadratic functions One of the simplest kinds of functions that exhibit
... characteristic shape, a curve called a parabola. A parabola has a fixed concavity (always up, or always down) across its entire domain, which according to the formula is (in the absence of a modeling situation) the set of all real numbers. If a > 0 (a is called the leading coefficient), then the cur ...
... characteristic shape, a curve called a parabola. A parabola has a fixed concavity (always up, or always down) across its entire domain, which according to the formula is (in the absence of a modeling situation) the set of all real numbers. If a > 0 (a is called the leading coefficient), then the cur ...
04-function
... R (real numbers) is uncountable • Intuition: P(Z+) is uncountable and is a “subset” of R. • There is a injection from P(Z+) to R: Input: a subset of Z+, S={s1, s2, s3,…} Output: a real number X in [0,1] such that X=0.x1x2x3x4… ...
... R (real numbers) is uncountable • Intuition: P(Z+) is uncountable and is a “subset” of R. • There is a injection from P(Z+) to R: Input: a subset of Z+, S={s1, s2, s3,…} Output: a real number X in [0,1] such that X=0.x1x2x3x4… ...
What is. . . an L-function? - Mathematisch Instituut Leiden
... (2) from automorphic forms and automorphic representations. We call L-functions arising in this way arithmetic or automorphic, respectively. In many cases, arithmetic L-functions can be shown to be automorphic. This is useful because an L-function defined by a Dirichlet series (1.7) is a priori only ...
... (2) from automorphic forms and automorphic representations. We call L-functions arising in this way arithmetic or automorphic, respectively. In many cases, arithmetic L-functions can be shown to be automorphic. This is useful because an L-function defined by a Dirichlet series (1.7) is a priori only ...
Special Products of Polynomials
... CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-qualit ...
... CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-qualit ...
Pre-Calculus
... trigonometric form, and multiply complex numbers in trigonometric form. 5 State, probe, and use De Moivre's theorem. Standard 7 Sequences and Series 1 Understand and use summation notation. 2 Find sums of infinite geometric series. 3 Prove the sum formulas for arithmetic series and for finite and in ...
... trigonometric form, and multiply complex numbers in trigonometric form. 5 State, probe, and use De Moivre's theorem. Standard 7 Sequences and Series 1 Understand and use summation notation. 2 Find sums of infinite geometric series. 3 Prove the sum formulas for arithmetic series and for finite and in ...
