Contact information
Name:
C. Jayne Trent
Email:
trentj@lafayette.edu
When:
Thursday, April 30, 2026 - 12:15pm - 1:10pm
Where:
Pardee 217
Presenter:
Asimina Hamakiotes, Fordham University
Price:
Free and there will be pizza!
Abstract: For a positive integer d, let p_d(n) := 0^d + 1^d + … + n^d; i.e., p_d(n) is the sum of the first d-th powers up to n. It’s well known that p_d(n) is a polynomial of degree d+1 in n. While this is usually proved by induction, once d is not small it’s a challenge as one needs to know the polynomial for the inductive step. In this talk, we show how this difficulty can be bypassed by giving a simple proof that p_d(n) is a polynomial of degree d+1 in n by using L’Hopital’s rule, and show how we can then determine the coefficients by Cramer’s rule.
Sponsored by:
Dept. of Mathematical Sciences