Question

prove by induction that 2^n is less or equal to n!

Answer 1

a set of positive numbers whose square is 25

Answer 2

what?

Answer 3

mmmm im not sure but i wrote a test about it eash it dealt with me

Answer 4

if n = 1 then 2 < = 2!=2.
If we have for n = k that 2^k <= k!. Then for n = k+1 we will have 2^(k+1) = (2^k)*2 <=k!*(k+1) = k!.
what we wanted.

Answer 5

true!!!!

Answer 6

basis step: for n>=4 , 2^n<=n!

Inductive step: assume that if k=4, p(k) is true. {2^4<=4!}
for k>=0, we show that if 2^k<=k!, then 2^(k+1)<=(n+1)!

2^(k+1) = 2*2^k <=2*k!
<(k+1)k! = (k+1)!