# Problem of the Month

- Everyone is welcome to participate, but only undergraduate OU students are eligible for the prizes.
- If there is more than one correct submission, the evaluation committee will select a winner.
- 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).
- Make sure that your submission includes your name and OU email.
- The deadline for submission is the last day of the month.

### November 2019

## Breaking into small pieces

Show that for every natural number \(k>1\) there exist natural numbers \(n\) and \(m\) with \(n>m\) such that \[ \frac{1}{k} = \frac{1}{m(m+1)} + \frac{1}{(m+1)(m+2)} + \cdots + \frac{1}{n(n+1)} \]