European Journal of Molecular & Clinical Medicine
2515-8260
7
11
2020
12
24
Generalization of sum of positive integral powers of natural numbers
749
757
5271
EN
B.Mahaboob,Y.Harnath,C.Narayana,V.B.V.N.Prasad, Y. Hari Krishna,
G.Balaji Prakash
Journal Article
2020
12
24
<em>Sum of positive integral powers of first n natural numbers has been an interesting problem for many years. </em><em>Mathematicians, students and research scholars have been attempting to crack this problem for decades. The primary objective of this talk is to generate a generalized result for an ancient interesting problem in the research field of Analytic Number Theory. That problem states that sum of k<sup>th</sup> powers of first n- natural number coincides with a unique a polynomial of degree (k+1) in n over natural numbers. The existence and uniqueness of this polynomial are established using the principles of Linear Algebra. The innovative result derived here opens a way to write the formula for the sum of any positive integral power of first n- natural numbers.</em>
https://ejmcm.com/article_5271_880114c50955da16c54e4ceaddad56f9.pdf