Deptals

Question 1

What is Mathematical Induction?

Answer 1

A technique used to prove a statement is true for every natural number

Question 2

What is the first step in Mathematical Induction?

Answer 2

P(1)

Question 3

3.What does the Basis Step in a Mathematical
Induction Provide?

Answer 3

A starting point for the induction

Question 4

4. What is proven in the Inductive Step of
   mathematical induction?

Answer 4

The statement holds for the next case, given it
holds for a particular case

Question 5

5. In a mathematical induction proof, what comes after the inductive hypothesis is made?

Answer 5

Proving the statement for k + 1

Question 6

6. Why is the inductive hypothesis important in
   mathematical induction?

Answer 6

It establishes an initial foothold

Question 7

7. Why might a mathematician choose to use
   mathematical induction?

Answer 7

To prove the statement for an infinite number of cases

Question 8

8. What is the term for the statement you are trying to prove in a mathematical induction or strong induction proof.

Answer 8

Inductive hypothesis

Question 9

9. What are the limitations of mathematical
   induction?

Answer 9

Limited to proving statements about natural
numbers

Question 10

10. Which of the following can be proven using
    mathematical induction?

Answer 10

2^n is an even number for positive integers n.

Question 11

11. Is a type of induction in which we assume all of the previous values of k.

Answer 11

Strong Induction

Question 12

12. Prove that given any integer for n, n3 + 2n will be divisible by 3.

Answer 12

3 * (m + k^2 + k + 1) is divisible by 3

Question 13

13. What does the Inductive Step in mathematical induction assume and prove?

Answer 13

a) Assumes the statement holds for an integer k
and proves it for k +

Question 14

14. Why is it important to know the least element in mathematical induction?

Answer 14

c) Because in mathematical induction, you must
start with the least element

Question 15

15. The two steps involved in proving mathematical statements are the base step and inductive step.

Answer 15

a) True

Question 16

16. What is the primary concept behind recursion?

Answer 16

b) Breaking down a problem into smaller, simpler

Question 17

17.. Which of the following best describes a
self-referential manner in recursion?

Answer 17

b) A function calling itself with simpler input values

Question 18

18. Why is recursion considered important in
    solving complex problems?

Answer 18

c) It breaks down complex problems into simpler similar sub-problems

Question 19

19. How does recursion often impact code
    simplicity?

Answer 19

c) It makes code more straightforward and easier to read

Question 20

20. What is the base case for the recursive
    definition of factorial?

Answer 20

c) 0! = 1

Question 21

21. In sequences, how is recursion often utilized?

Answer 21

b) To define sequences

Question 22

22. What does an explicit formula do?

Answer 22

a) Defines the nth term independently of previous terms

Question 23

23. In geometric sequences, what remains
    constant?

Answer 23

c) The ratio between consecutive terms

Question 24

24. What is a recurrence relation?

Answer 24

c) A method of defining a sequence where each
term is a function of the preceding term

Question 25

25. What is a recursive definition?

Answer 25

d) A definition where an object is defined in terms of itself, in simpler form