Question: In Chapter we learned Gauss's trick for showing that for all positive integers n,
1 + 2 + 3 + 4 + . . . + n = {n(n + 1)/2}
Use the technique of asserting that if there is a counter-example, there is a smallest counter-example and deriving a contradiction to prove that the sum is n(n + 1)/2. What implication did you have to prove in the process?