I don't get it. How does $\sum\_{j=1}^m\frac{1}{m}=1$? This looks like a harmonic series. I got this from brilliant.org, the website that trains students for AMC, AIME, Olympiad type of problems. This was the original problem:
[![enter image description here](https://i.stack.imgur.com/Lc6Mb.png)](https://i.stack.imgur.com/Lc6Mb.png) and this was the solution: [![enter image description here](https://i.stack.imgur.com/KgpW4.png)](https://i.stack.imgur.com/KgpW4.png)   
 I just don't get this part: [![enter image description here](https://i.stack.imgur.com/SkMjT.png)](https://i.stack.imgur.com/SkMjT.png) I deeply apologize if its something trivial. Its been a while since my last math class in linear algebra. Any hint would be appriciated!