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Use the Well Ordering Principle (WOP) to show that 1+2+3+···+n= n(n+1)2 for all n ∈ N....

Use the Well Ordering Principle (WOP) to show that

1+2+3+···+n= n(n+1)2

for all n ∈ N.

Hint: In general, proofs using the WOP take the following format: proceed by contradiction and find a nonempty set of counterexamples, C, to the statement. The WOP is applied to C to find the smallest element. A contradiction is reached (somehow), which implies that C must actually be empty.

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