When does a sum have an answer?

Nov 21 2022, 7:00pm in Hill 705

Speaker: Robert Dougherty-Bliss

Abstract: Many sums have an answer, like 1+2+…+n. How do we find these answers? Do all sums have answers? For example, does 1!+2!+…+n! have an answer? What is an "answer" anyway?

These questions are analogous to what you learn to ask in Calculus II: which integrals have answers, and how do you find them? Fortunately, the state of affairs for summation is much nicer. Unfortunately, it is less known to most people! I will try to rectify that by showing us some summation techniques and answering a few of the above questions.