Question: 3. [18 marks] Prove the following theorems using weak induction: a. [6 marks] Vne Z, Voelt, (n 20An > 2) + (a - 1|a -1).

3. [18 marks] Prove the following theorems using weak induction: a. [6 marks] Vne Z, Voelt, (n 20An > 2) + (a - 1|a" -1). b. [6 marks] For any convex n-sided polygon p (n 2 3) inscribed in a circle, p can be maximally triangulated using 2n - 3 non-intersecting chords. See the below figure for an example of an inscribed pentagon (n = 5) triangulated using seven non-intersecting chords. Note: you may include a figure to support your proof, but you must still write your justifica- tions clearly in text. c. [6 marks] Let S1 = 25, and let Sat1 =8 . VS, +5. Prove for all n 2 1, that S,,

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