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Extracted text: Section 3.1 Homework 13 +23+... +n = 1n (n +1) for all natural numbers n. 1. 1 + ... + 1 1 1 + for all natural + 2. n(n+1) (n+1) 1(2) (2)3 3(4) 1-r* n 1 and any ne N for any r 3. Show thatr" 1-r k=0 1+2+22 +... + 2"- = 2" -1 for all natural numbers n. 4. 52 -1 is a multiple of 8 for all natural numbers n 5. 9" - 4" is a multiple of 5 for all natural numbers n 6. Use induction to prove Bernoulli's inequality: If 1 + x > 0, the 7. 1 Prove the Principle of Strong Induction: Let P(n) be a statement that is either true or false for each na Then P(n) is true for all n, provided that (a) P(1) is true (b) For each natural number k, if P(i) is true for all integers j s 8. 7444/ )2