dattranvan22
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- Joined
- Nov 30, 2015
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I have some a lesson exercise. I don't know how do that. Can you help me solve it?
1. Prove that 2015^0 + 2015^1 + 2015^2 + ... + 2015^n = (2015^(n +1) −1)/2014 by using induction.
2. Prove that 2^2n − 1 is divisible by 3 for all integers n ≥ 0 by using induction.
3. Give a recursive definition of the sequence a n, n = 1, 2, 3, ... if a n = 6n − 1.
4. MAC address of network card is represented by Hexadecimal. If they use 12 digits to assign MAC address, how many network card can be assigned using Hexadecimal without duplication?
6. A small company has 13 departments of total 190 employees. Each department has maximum 15 employees. Each month, each department organize a birthday party for all employees in the department that has birthday in that month. Prove that there is at least 1 month that has at least 2 birthday parties by 2 departments.
7. Show steps by steps of how to generate the next permutation of 231456?
8. Roll a fair die 10 times. X is assigned to the number appears, Y is assigned to 0 if number is odd and to the number of it is even. Calculate E(X), E(Y), V(X), V(Y).
9. Choose any topic introduced from chapter 5 to 12 and study the relation of that topic in discrete maths with computer science or information technology. Summary into 1 or 2 paragraphs with at least 15 sentences.
1. Prove that 2015^0 + 2015^1 + 2015^2 + ... + 2015^n = (2015^(n +1) −1)/2014 by using induction.
2. Prove that 2^2n − 1 is divisible by 3 for all integers n ≥ 0 by using induction.
3. Give a recursive definition of the sequence a n, n = 1, 2, 3, ... if a n = 6n − 1.
4. MAC address of network card is represented by Hexadecimal. If they use 12 digits to assign MAC address, how many network card can be assigned using Hexadecimal without duplication?
6. A small company has 13 departments of total 190 employees. Each department has maximum 15 employees. Each month, each department organize a birthday party for all employees in the department that has birthday in that month. Prove that there is at least 1 month that has at least 2 birthday parties by 2 departments.
7. Show steps by steps of how to generate the next permutation of 231456?
8. Roll a fair die 10 times. X is assigned to the number appears, Y is assigned to 0 if number is odd and to the number of it is even. Calculate E(X), E(Y), V(X), V(Y).
9. Choose any topic introduced from chapter 5 to 12 and study the relation of that topic in discrete maths with computer science or information technology. Summary into 1 or 2 paragraphs with at least 15 sentences.
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