Problem of the Month

• Everyone is welcome to participate, but only undergraduate OU students are eligible for the prizes.
• At the end of the academic year, a prize will be awarded to the undergraduate OU students with the most correct solutions.
• A complete solution to the problem must include a proof.
• Solutions to the Problem of the Month can be submitted in the Math Department's office (PHSC 423), or via email to nickmbmiller [at] ou [dot] edu
• Make sure that your submission includes your name and OU email.
• The deadline for submission is the last day of the month.
• The problem of the month during the summer months of May, June, July, and August will not be graded and are just for fun.

Winners of the academic year 2023/24 is Jacob Norris.

March 2025

March sequences

Suppose that k_n is an infinite sequence of real numbers, indexed by the natural numbers, for which k₁>1 and such that k₁+k₂+...+k_n<2k_n for every n. Show that there exists a real number q>1 having the property that qⁿ < k_n for all n.