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INDUCTION 1. Prove that for any integer n, n(n2-1)(n+ 2) is divisible by 4. 2. Prove that for any integers n>=1, n(5n-3) 1+6+11+16+ + (5n-4) - 2 3. Prove that for all integers n >=2, 2 4. Prove that for all integers, I + 1 + + 1 = 1.2 2.3 n(n+1) n+1 5. Prove that for all integers, 2 2² 2 + + n 6. There is a relationship between the number of vertices in a polygon and the number of triangles in any triangulation of that polygon. State this relationship and prove it by induction.

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