A generalization due to Ramanujan of Faulhaber's formula
Time and place
1 PM on Thursday, June 25th, 2020;
Cesar Valverde (Medgar Evers College (CUNY))
Abstract
For k a positive integer, Faulhaber's formula gives the sum from i=1 to i=n of i^k. After exploring this formula, we will explain Ramanujan's generalization to a couple of cases where k=m/2 for m a positive odd integer, and we will conjecture what a general formula may look like and what may be required to give an elementary proof of it.
