# Thread: Prove that there is a unique positive integer greater than 1 that equals

1. ## Prove that there is a unique positive integer greater than 1 that equals

I don't know how to solve this problem.

Prove that there is a unique positive integer greater than 1 that equals

the sum of the positive integers less than it.

I started of as

condition 1: n>1

condition 2: sum = n - 1

I'm stuck

2. Originally Posted by HelpMehPlz
I don't know how to solve this problem.

Prove that there is a unique positive integer greater than 1 that equals

the sum of the positive integers less than it.

I started of as

condition 1: n>1

condition 2: sum = n - 1

I'm stuck
The second condition is : $\displaystyle n = (n-1)+(n-2)+(n-3)+...+1$.

3. Originally Posted by HelpMehPlz
Prove that there is a unique positive integer greater than 1 that equals
the sum of the positive integers less than it.
$\displaystyle M = \sum\limits_{k = 1}^{M - 1} k = \frac{{\left( {M - 1} \right)M}} {2}\; \Rightarrow \;M = 3$