Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to solve this equation?

This what I reached with my equality equation, but I could not continue: $$\frac{2n}{2} = \frac{n(n+1)}{6}$$

share|cite|improve this question
Have you tried some numbers? – Raskolnikov Apr 4 '12 at 7:48
Yes, do some work. Try Wolfram, it will solve it for you without any effort. – copper.hat Apr 4 '12 at 8:12

First simplify $2n/2$ to $n$. Then multiply through by $6$ to get rid of the fractions: $6n=n(n+1)$. There are several ways to proceed from here. The neatest, perhaps, is to notice that this is certainly true when $n=0$, so that’s one solution. If $n\ne 0$, we can divide both sides by $n$ to get $6=n+1$, or $n=5$; this is the only other solution.

The straightforward, by-the-book approach is to bring everything to one side of the equation to get $n^2-5n=0$. The lefthand side factors as $n(n-5)$, so you have $n(n-5)=0$. The product of two real numbers is $0$ if and only if at least one of the two numbers is $0$, so this equation is satisfied only when $n=0$, $n-5=0$, or both $-$ i.e., when $n=0$ or $n=5$, just as we saw before. (Of course it’s not possible for $n$ and $n-5$ to be $0$ simultaneously, so the both option doesn’t apply here.)

Of course you can also use the quadratic formula to solve $n^2-5n=0$, but it would be a great waste of time and effort when the factorization of the lefthand side is so obvious.

share|cite|improve this answer
From you brought this n2−5n=0, (or how)? – SolidUs Apr 4 '12 at 8:01
@SolidUs: You have $6n=n(n+1)$. Multiply out the righthand side: $6n=n^2+n$. Now subtract $6n$ from both sides: $0=n^2+n-6n=n^2-5n$. – Brian M. Scott Apr 4 '12 at 8:06

2n/2 =n as the 2 gets cancelled out.

So you get n =n(n+1)/6 ie. 6n=n2 + n

now collect all the terms together on the R.H.S

n2 -5n = 0

factorizing we get :

n(n-5) = 0

Now if the product of 2 numbers is 0 then atleast one of them must be 0

so either n = 0 or n - 5 = 0

which gives you : n=0 or n=5

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.