Add to ORKGThe formulae to obtain the sum of the first n natural numbers, the sum of the squares of the first n natural numbers and the sum of the cubes of the first n natural numbers are generally introduced to students during their final school year. Generally, these formulae are derived using the celebrated technique of mathematical induction. But the defect of this approach is that we must know in advance the formula to be proved. This is clearly a great handicap
The thesis discusses classical number theory problems on representations of integers by sums of two,...
Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, a...
An induction proof of a formula consists of three parts:a) Show the formula is true for n=1; b) Assu...
Now in Part II of the article, we present a unified approach by which the formula for the sum of th...
Students typically encounter the formulas n∑ i=1 i = n(n+ 1) 2 n∑ i=1 i2 = n(n+ 1)(2n+ 1) 6 n∑ i=1 i...
summary:In this article, the formula of the sum of the first n natural numbers is derived and then i...
An investigation of the origin of the formulas for the sums of integer powers was performed. A metho...
Introduction This paper deals with the sums of products of first n natural numbers, taken r at a tim...
Let n;k be positive integers (k> 1), and let Sn(k) be the sum of the n-th powers of positive inte...
This thesis is an exposition on some attributes of the sums of powers of the first n positive intege...
We investigate the number of representations of an integer as the sum of various powers. In particul...
Using geometric arguments, we prove the well-known formula for the sum of the first n integers squar...
In this paper, we present several different approaches to formula for the sum of integer powers of t...
In is described for finding a formula for the sum of the powers of the first the companion article b...
any “higher ” parabola and Roberval wrote back to say that he had discovered the same thing by using...
The thesis discusses classical number theory problems on representations of integers by sums of two,...
Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, a...
An induction proof of a formula consists of three parts:a) Show the formula is true for n=1; b) Assu...
Now in Part II of the article, we present a unified approach by which the formula for the sum of th...
Students typically encounter the formulas n∑ i=1 i = n(n+ 1) 2 n∑ i=1 i2 = n(n+ 1)(2n+ 1) 6 n∑ i=1 i...
summary:In this article, the formula of the sum of the first n natural numbers is derived and then i...
An investigation of the origin of the formulas for the sums of integer powers was performed. A metho...
Introduction This paper deals with the sums of products of first n natural numbers, taken r at a tim...
Let n;k be positive integers (k> 1), and let Sn(k) be the sum of the n-th powers of positive inte...
This thesis is an exposition on some attributes of the sums of powers of the first n positive intege...
We investigate the number of representations of an integer as the sum of various powers. In particul...
Using geometric arguments, we prove the well-known formula for the sum of the first n integers squar...
In this paper, we present several different approaches to formula for the sum of integer powers of t...
In is described for finding a formula for the sum of the powers of the first the companion article b...
any “higher ” parabola and Roberval wrote back to say that he had discovered the same thing by using...
The thesis discusses classical number theory problems on representations of integers by sums of two,...
Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, a...
An induction proof of a formula consists of three parts:a) Show the formula is true for n=1; b) Assu...