1.)Suppose that you must prove the following fact using mathematical induction: For all n4, P(n) is true. What must be proven in the base case?

a)

P(1)

b)

P(4)

c)

P(2)

d)

P(3)

2.)Suppose that you must prove the following fact using mathematical induction: For all n4, P(n) is true. What is the inductive hypothesis in the inductive step?

a)	P(n+1) is true

b)	P(4) is true

c)	P(n) is true

d)	P(1) is true

3.)Suppose that you must prove the following fact using mathematical induction: For all n4, P(n) is true. What must be proven in the inductive step?

a)

P(1)

b)

P(4)

c)

P(n+1)

d)

P(n)

4.)Define P(n) to be the assertion that:

j=1nj2=n(n+1)(2n+1)6

P(3) = ?

a)

b)

c)

d)

5.) To prove that for n 1, j=1n1j221n

if we have proved that for k1,j=1k1j221k, what must be proved in the inductive step?

a)

b)

c)

d)