precalculus

can you check my answer?

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

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  1. since we're dealing with powers of 2, I'd pick B

    Besides, if k>1, (k+1) ≯ (k+k)

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