Discrete Maths – Exercises MULTIPLE CHOICE – JUST ONE OF THE AVAILABLE ANSWERS IS TRUE. 1....

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Discrete Maths – Exercises MULTIPLE CHOICE – JUST ONE OF THE AVAILABLE ANSWERS IS TRUE. 1. According to this inequalities: What can we say? a) They are both true; b) Inequality i is always false; c) Inequality ii is always false; d) The truth of this inequalities depends on n value. 2. If , so is equal to: 3. According to the sequence , consider the following affirmations: i. matches the sequence defined by ii. Each term of the given sequence is multiple of 5. a) Both of the affirmations are false; b) The affirmation i is true but ii is false; c) The affirmation ii is true but i is false; d) Both of the affirmations are true. 4. Is the following expression true or false? Explain. If , so for any natural number n >= 1, 5. We have the following equality: Using the telescopic series method, prove that 6. Prove that 6.1 Assuming X is a set with more than 2 elements, calculate the result of the following sum: 7. We know that Prove that 8. We have the sequences an and bn: Using the mathematics induction method prove that this sequences have a recurrence relation: for

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Discrete Maths – Exercises MULTIPLE CHOICE – JUST ONE OF THE AVAILABLE ANSWERS IS TRUE. According to this inequalities: What can we say? They are both true; Inequality i is always false; Inequality ii is always false; The truth of this inequalities depends on n value. If , so is equal to: According to the sequence , consider the following affirmations: matches the sequence defined by Each term of the given sequence is multiple of 5. Both of the affirmations are false; The affirmation i is true but ii is false; The affirmation ii is true but i is false; Both of the affirmations are true. Is the following expression true or false? Explain. If , so for any natural number n >= 1, We have the following equality: Using the telescopic series method, prove that Prove that Assuming X is a set with more than 2 elements, calculate the result of the following sum: We know that Prove that We have the sequences an and bn: Using the mathematics induction method prove that this sequences have a recurrence relation: for

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David · Accepted Answer

Discrete Mathematics – Exercises
MULTIPLE CHOICE – JUST ONE OF THE AVAILABLE ANSWERS IS TRUE 
1. According to this inequalities:
What can we say? 
a) They are both true; 
b) Inequality i is always false; 
c) Inequality ii is always false; 
d) The truth of these inequalities depends on n value. 
Solution: Both the inequalities are true.  
When we keep the value of n = 1  
 
2
1
1
1
1
3






 
 kk
kk  
 11  
Similarly, through mathematical induction for all the values of n the inequalities holds equal. 
Thus both inequalities are true.
2. If , so   is equal to:
Solution: The forward difference operator, kkk aaa  1 .  
 












 
 
1
1
)1(
1
)1( 1
k
n
k
n
a kkk   
 




















 

1
11
)1(
k
n
k
n
a kk  
By Pascal’s identity,  
 






k
n
a kk )1(
3. According to the sequence , consider the following 
affirmations:
i.  matches the sequence defined by
ii.         Each term  of the given sequence is multiple of 5. 
What can we say? 
 a) Both the affirmations are false. 
 b) The affirmation i is true but affirmation ii is false. 
 c) The affirmation ii is true but affirmation i is false.

Discrete Maths – Exercises MULTIPLE CHOICE – JUST ONE OF THE AVAILABLE ANSWERS IS TRUE XXXXXXXXXXAccording to this inequalities: What can we say? a) They are both true; b) Inequality i is always...

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