Polynomials

Polynomials calculating sums of powers of arithmetic progressions

The polynomials calculating sums of powers of arithmetic progressions are polynomials in a variable that depend both on the particular arithmetic progression constituting the basis of the summed powers and on the constant exponent, non-negative integer, chosen. Their degree always exceeds the constant exponent by one unit and have the property that when the polynomial variable coincides with the number of summed addends, the result of the polynomial function also coincides with that of the sum. The problem therefore consists in finding i.e. polynomials as a function of calculating sums of addends: with and integers positive, first term of an arithmetic progression and the common difference.The two parameters can be not only integers but also rational, real and even complex. (Wikipedia).

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Finding the sum or an arithmetic series using summation notation

👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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Math tutorial for determining the sum of an arithmetic series

👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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Finding the sum of a series arithmetic

👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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Evaluating the partial sum of a arithmetic series

👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

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Determine the Function for the Sum of a Power Series (e to the power of x)

This video explains how to determine the sum of a power series. Site: http://mathispower4u.com

From playlist Power Series

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What is the sum of an arithmetic series using the sum formula

👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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Learn how to find the sum of an arithmetic series

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From playlist Series

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Linear Equations in Primes and Nilpotent Groups - Tamar Ziegler

Tamar Ziegler Technion--Israel Institute of Technology January 30, 2011 A classical theorem of Dirichlet establishes the existence of infinitely many primes in arithmetic progressions, so long as there are no local obstructions. In 2006 Green and Tao set up a program for proving a vast gen

From playlist Mathematics

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From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra

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From playlist Mathematics

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Interpreting Polynomial Structure Analytically - Julia Wolf

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From playlist Precalculus and Algebra

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Jacob Bernoulli | Arithmetic progression | Faulhaber's formula | Polynomial | Bernoulli polynomials | Gnomon (figure) | Carl Gustav Jacob Jacobi | Ibn al-Haytham | Integer | Pierre de Fermat | Square number | Sums of powers | Pascal's triangle | Archimedes | Number theory