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Usage on de.wikiversity.org Kurs:Einführung in die Algebra (Osnabrück 2009)/Vorlesung 12; Kurs:Vorkurs Mathematik (Osnabrück 2009)/Vorlesung 5; Kurs:Mathematik (Osnabrück 2009-2011)/Teil I/Vorlesung 5; Kurs:Mathematik für Anwender (Osnabrück 2011-2012)/Teil I/Vorlesung 3; Kurs:Analysis (Osnabrück 2013-2015)/Teil I/Vorlesung 3
The case α = 1 gives the series 1 + x + x 2 + x 3 + ..., where the coefficient of each term of the series is simply 1. The case α = 2 gives the series 1 + 2x + 3x 2 + 4x 3 + ..., which has the counting numbers as coefficients. The case α = 3 gives the series 1 + 3x + 6x 2 + 10x 3 + ..., which has the triangle numbers as coefficients.
The first four partial sums of the series 1 + 2 + 3 + 4 + ... The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...
The Professor's Cube (also known as the 5×5×5 Rubik's Cube and many other names, depending on manufacturer) is a 5×5×5 version of the original Rubik's Cube. It has qualities in common with both the 3×3×3 Rubik's Cube and the 4×4×4 Rubik's Revenge , and solution strategies for both can be applied.
Place two points on two adjacent edges of a unit cube, each at a distance of 3/4 from the point where the two edges meet, and two more points symmetrically on the opposite face of the cube. Then these four points form a square with side length 3 2 4 ≈ 1.0606601. {\displaystyle {\frac {3{\sqrt {2}}}{4}}\approx 1.0606601.}
In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x 3 = 2; in other words, x = , the cube root of two. This is because a cube of side length 1 has a volume of 1 3 = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2.
It can be proven that: . For a given prime number p, if n is p-perfect and p does not divide n, then pn is (p + 1)-perfect.This implies that an integer n is a 3-perfect number divisible by 2 but not by 4, if and only if n/2 is an odd perfect number, of which none are known.
Here is an example of polynomial division as described above. Let: = +() = +P(x) will be divided by Q(x) using Ruffini's rule.The main problem is that Q(x) is not a binomial of the form x − r, but rather x + r.