Question: 1. Write the first four terms of the sequence defined by the following explicit formula (just give the specific formulas; don't bother doing the arithmetic):

1. Write the first four terms of the sequence defined by the following explicit formula (just give the specific formulas; don't bother doing the arithmetic): 2. Give an explicit formula for the sequence: 3. (This Problem Counts Double) 4. Given the following original summation: Write the original summation in expanded form: Separate off the final term from the original summation: 5. Write the following sum using summation (sigma) notation: 6. Give a simpler but equivalent expression for 7. Give the standard recursive definition of n! for n 0: 8. Transform the following expression by making the change of variable j = k + 2: 9. Use the formula for the sum of the first n integers to calculate: 6+7+8+...+65 10. Use the formula for the sum of a geometric sequence to calculate: HINT: 11. (THIS PROBLEM COUNTS DOUBLE) 12. Give an Inductive Proof that for all integers n 1: 2 + 6+ 10 +...+ (4n - 2) = 2n2 13. (THIS PROBLEM COUNTS DOUBLE) 14. Prove the following conjecture using Mathematical Induction: 15. (THIS PROBLEM COUNTS DOUBLE) 16. Give an Inductive Proof that n2 + n is even for all integers n >= 1

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