However you come up with the answer could you please explain how you came to it?

Question

However you come up with the answer could you please explain how you came to it? Even if it's a definition please

1. If the kth odd positive integer is represented by 2k-1, then what is the (k+1)th odd positive integer represented by?

a. 2k

b. 2k+1

c. 2k+2

d. k2+1

e. (k+1)2

2. If you want to use mathematical induction prove the 2n > n2 for n a , then what will n be equal to in the basis step (i.e. what is the value of a?)

a. 1

b. 2

c. 3

d. 4

e. 5

3. Which of the following expressions is the same as 1/3n+1?

a. 1/3n+1 + 2/3n+1

b. 1/3n - 2/3n+1

c. -1/3n + 2/3n+1

d. -1/3n+1 - 2/3n

e. 1/3n+1 + 1/3n+1

4. The condition under which a recursive function does NOT have to make a call to itself is referred to as what?

a. Base Case

b. Basis Step

c. Recursive Case

d. Inductive Step

e. Inductive Case

5. If you want to use mathematical induction to prove that (n+2) < n2 for n a , then what will n be equal to in the basis step (i.e. what is the value of a?)

a. 0

b. 1

c. 2

d. 3

e. 4

6. If the kth term of a sequence is given by k*2k-1, then what is the (k+1)th term of the sequence given by?

a. (k+1)*2k+1

b. (k+1)*2k-1

c. (k+1)*2k

d. k*2k+1

e. k*2k

7. Which of the following describes what should be shown to be true in the “Inductive Step” of a mathematical induction proof?

a. P(1) P(k+1)

b. "k(P(1) P(k)) P(k+1)

c. [P(1) P(2) … P(k)] P(k+1)

d. P(1) "k(P(k) P(k+1))

e. "k(P(k) P(k+1))

8. What is the smallest positive integer for which the inequality n! < ((n+1)/2)n is true?

a. 1

b. 2

c. 3

d. 4

e. 5

9. What function can be executed recursively to implement the product n*5, where positive integer?

a. k*k*k*k*k

b. 5 + k*5

c. 5 – k*5

d. k*5

e. k^5

10. What is distinctive about a recursive program?

a. It has an infinite loop

b. It has only one loop

c. It has no output

d. It has no inputs

e. It calls itself

I'm not sure if I selected the correct subject.

Explanation / Answer

1. If the kth odd positive integer is 2k-1

Then (k+1)the will be 2(k +1) - 1 = 2k + 2 - 1 = 2k+1

Option b is correct.

2. If we want to prove 2n > n2

In first step., if we take n= 1 then the result holds.

i.e 2(1) > (1)2 => 2 >1

option a is correct.

3. There is some mistake. None of the options matches with the expression given.

5. n=3 option d. for which (n+2)< n2 will hold true. As 5< 9

6. If kth term is k*2k -1

then (k+1)th term will be (k+1)*(2(k+1) -1) = (k+1)* 2k +2 -1

= (k+1)* 2k +1

Option A

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