# Principle of Mathematical Induction

1. What is the base case for the inequality 7n > n3, where n = 3?
a) 652 > 189
b) 42 < 132
c) 343 > 27
d) 42 <= 431

2. In the principle of mathematical induction, which of the following steps is mandatory?
a) induction hypothesis

b) inductive reference
c) induction set assumption
d) minimal set representation

3. For m = 1, 2, …, 4m+2 is a multiple of ________
a) 3
b) 5
c) 6
d) 2

4. For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________
a) m2+3
b) m+1
c) mm
d) 3m2+4

5. For every natural number k, which of the following is true?
a) (mn)k = mknk
b) m*k = n + 1
c) (m+n)k = k + 1
d) mkn = mnk

6. By induction hypothesis, the series 12 + 22 + 32 + … + p2 can be proved equivalent to ____________
a) p2+27
b) p(p+1)(2p+1)6
c) p∗(p+1)4
d) p+p2

7. For any positive integer m ______ is divisible by 4.
a) 5m2 + 2
b) 3m + 1
c) m2 + 3
d) m3 + 3m

8. According to principle of mathematical induction, if P(k+1) = m(k+1) + 5 is true then _____ must be true.
a) P(k) = 3m(k)
b) P(k) = m(k) + 5
c) P(k) = m(k+2) + 5
d) P(k) = m(k)

9. Which of the following is the base case for 4n+1 > (n+1)2 where n = 2?
a) 64 > 9
b) 16 > 2
c) 27 < 91
d) 54 > 8

.10. What is the induction hypothesis assumption for the inequality m ! > 2m where m>=4?
a) for m=k, k+1!>2k holds
b) for m=k, k!>2k holds
c) for m=k, k!>3k holds
d) for m=k, k!>2k+1 holds