5.55. Disprove the statement: There exist odd integers a and b such that 4 | (3a2 + 7b2). 5.56. Disprove the statement: There is a real number x such that x+x+1 = 2x2. 5.57. Disprove the statement: There is an integer n such that n2 + n3 + n2 + n is odd. 6.11. Prove that +++(k+3)= for every positive integer n. 6.12. Consider the open sentence P(n): 9+13++ (4n+5)=4141, where n € N. (a) Verify the implication P(k) P(k + 1) for an arbitrary positive integer k. (b) Is Vn N, P(n) true? 162 Chapter 6 Mathematical Induction 6.13. Prove that 1-11+2-21++nn! (n+1)!-1 for every positive integer n. 6.14. Prove that 2! 4!-6! (2n)! [(n+1)!]" for every positive integer n. 6.15. Prove that ++++ |≤2√√ for every positive integer n. 6.16. Prove that 7 | [34+1-52-11 for every positive integer n. 6.18. Prove that 2">3 for every integer n> 10. 6.21. Prove that 4 | (5"-1) for every nonnegative integer n. 6.22. Prove that 3">n2 for every positive integer n. 6.23. Prove that 7 (32-2") for every nonnegative...

Solve every question correctly and show the work.

FIND A PARAMETRIC REPRESENTATION and sketch the path Upper half of |z-2+i| from (4, -1) to (0, -1)

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