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

• Feb 5th 2009, 02:19 PM
HelpMehPlz
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
• Feb 5th 2009, 02:22 PM
Mush
Quote:

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 : $n = (n-1)+(n-2)+(n-3)+...+1$.
• Feb 5th 2009, 02:27 PM
Plato
Quote:

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.

$M = \sum\limits_{k = 1}^{M - 1} k = \frac{{\left( {M - 1} \right)M}}
{2}\; \Rightarrow \;M = 3$