**If you’ve ever taken a math class, it is highly likely that the teacher mentioned this seemingly random equation: (n(n-1))/2. But why does this formula exist? Some students may say because the answer is always even and some teachers may not give an explanation at all. This blog post will explain why n(n-1) = (n(n-1))/2 and how to prove it!**

**When doing math, there are several ways to look at seemingly complicated problems. While some may get lost in the process of solving a problem, others know that it’s all about finding different perspectives and angles. This is especially true when looking at strange equations like n(n-1). However, if you take a closer look and think outside of the box (or inside depending on how you view it), this equation becomes much simpler than what it seems. For example: If we write 4 x 3 = 12 and then subtract one from each side we can see that 2 x 2 = 4. So by multiplying both sides by two we can see that 2(2) – 1 = 4 – 1 which leaves us with an answer of 3 or 33**

**How many people get confused when they see that n(n-1) is even? I know it took me a while to understand why this was the case. While we are learning about exponents and multiplying and dividing, we don’t really think about how these apply in real life. As soon as you start looking at things like interest rates and other everyday math problems, you quickly realize that everything is an exponent! For instance, if you want to find out what two times three is for your five dollar bill, all you have to do is multiply 5 by 3 which equals 15 dollars. To figure out how much money would be left over after one year if someone invested $5 at ten percent interest rate compounded monthly for one year with no additional**

**The question, “Why is n(n-1) even?” has been asked by many students since the dawn of math. It was originally posed as a riddle to an Indian prince in 500 BC. The answer lies within this equation: “n”(n-1)=2n. This means that for every time you subtract one from the other, you get 2 more on either side of the equation.”**

**Can you believe it’s already Wednesday? I can’t. The days are just flying by and here we are, another week later than when we started the week off. It seems like all of our weeks go this way; they’re short but action packed! This past weekend was no different for me. On Saturday, I woke up early to get ready for a day trip with my family to Six Flags Great Adventure (one of the most popular amusement parks in NJ), which is about an hour away from where I live. However, on Sunday morning…I woke up 15 minutes before my alarm was set to ring at 6:30am – typical! But hey – maybe that means that Saturdays aren’t so bad after all 😉**T

**he author**

**The concept of factorials is a very important one to mathematics, and the specific case of n(n-1) has been seen in many different areas. It’s a simple idea that can be used to find a number quickly with no calculators. In this post we’re going to look at why the formula works using some examples from daily life.**