Can you check my answers?

Question

1.Which of the following shows the best next step to prove the following by mathematical induction?

3^n>n*2^n, n≥1
1.When n=1, the formula is valid because

3^1 1*2^1
3>2
2.Assuming that
3^k>k*2^k

a.3^k+1>k+1*2^k+1
b.3^k+1>k*2^k+1
c.4^k>k*3^k
d.3^k+1>(k+1)2^k+1

answer: A

2.Which of the following shows the best next step to prove the following by mathematical induction?

n!>2^n, n≥4

1. When n=1 the formula is valid because

4!>2^4
24>16
2.Assuming that k!>2^k
show that (k+1)!>2^k+1
(k+1)!=k!(k+1)

a.k!(k+1)>k!(k+k)
b.k!(k+1)>2^k(k+1)
c.k+1≥5
d.(k+k)>(k+1)!

answer:a