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Unformatted text preview: M325K Practice Exam 2
No Calculators, books, notes, etc. 1. Define the floor function. 2. State the Well-ordering Property. 3. Let r be a rational number. Under what conditions on r will r be rational? 4. Prove or disprove that the sum of two odd integers is even. 5. Find all primes of the form n2 + 2n - 3, where n is an integer, and show that you really do have all of them. 6. Prove or disprove that for a real number x, 2 x 2x . 7. Prove that 3 is irrational. 97 8. Compute the exact value of
n=1 (-1)n . n 9. Prove that
i=1 n2 = n(n + 1)(2n + 1) . 6 ...
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