4.6.4. Prove that for every n EN, +1 is divVisible by 10. 4.6.5. Prove that for any n EN, n° + 2n is divisible by 3. 4.6.6. Prove that for all n E N, 42n – 1 is divisible by 5. 4.6.7. Let a be an...

4.6.8

Extracted text: 4.6.4. Prove that for every n EN, +1 is divVisible by 10. 4.6.5. Prove that for any n EN, n° + 2n is divisible by 3. 4.6.6. Prove that for all n E N, 42n – 1 is divisible by 5. 4.6.7. Let a be an integer different than 1. Prove, by induction, that for any nEN, a" – 1 is divisible by a - 1 4.6.8. Prove that 1 1 + -n is an integer for any n E N. 4.6.9. Compute the following expressions (obtain a single number). 100 69 (a) E (&-(-1)*] (c) II: 2k-35 k31 200 99 (b) (d) II k+1 +1 k-2 i-10 4.6.10. Which of the following are true for any a1,..., an, b1,-. , bn E R? Justify Provide counterexamples for the false statements.