Great Deal! Get Instant \$10 FREE in Account on First Order + 10% Cashback on Every Order Order Now

# 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...

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 false; c) Inequality ii is always false; d) The truth of this inequalities depends on n value XXXXXXXXXXIf , so is equal to: XXXXXXXXXXAccording 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 XXXXXXXXXXIs the following expression true or false? Explain. If , so for any natural number n >= 1, XXXXXXXXXXWe have the following equality: XXXXXXXXXXUsing the telescopic series method, prove that XXXXXXXXXX6. Prove that XXXXXXXXXXAssuming X is a set with more than 2 elements, calculate the result of the following sum: 7. We know that Prove that XXXXXXXXXXWe have the sequences an and bn: XXXXXXXXXXUsing the mathematics induction method prove that this sequences have a recurrence relation: XXXXXXXXXXfor
Document Preview:

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: XXXXXXXXXXUsing 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

Answered Same Day Dec 29, 2021

## Solution

David answered on Dec 29 2021
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;
) 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.
d) Both...
SOLUTION.PDF