Exercises - The Well Ordering Principle

1. Prove the Archimedian property which states that if $a$ and $b$ are positive integers, then there exists some positive integer $n$ such that $na \ge b$.

2. Use the Well Ordering Principle to prove that the following statement is true for all positive integers $n$:
$$\sum_{i=1}^n i = \frac{n(n+1)}{2}$$

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