(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Proveby inductionthat

n!> 2^n for n[tex]\geq[/tex]4

2. Relevant equations

solved example:

P(n):2^n>1+3nlet n[tex]\geq[/tex]4

(base): n=4 2^4=16 > 13=1+12=1+(3)(4)

(implication): if for n=k: P(k): 2^k>1+3k, for k[tex]\geq[/tex]4

consider for n=(k+1):

2^(k+1)=2^k*2^1=2^k(1+1)=2^k+2^k >(1+3k) + (1+3k) for k[tex]\geq[/tex]4

>1+3k+3k

[tex]\geq[/tex]1+3k+12 > 1+3k+3

=1+3(k+1)

so P(k) => P(k+1)

3. The attempt at a solution

(Base) n=k

P(k): k!>2^k

(Implication) show P(k)=> P(k+1)

Consider: n=k+1

(k+1)! > 2^(k+1)

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

Please help if you can. I am confused. Thanx.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove by induction (discrete math's)

**Physics Forums | Science Articles, Homework Help, Discussion**