- #1
jonroberts74
- 189
- 0
Homework Statement
prove by induction[tex] 2^n < (n+2)!; \forall n \ge 0[/tex]
P(0)
[tex] 2^0 < (0+2)! [/tex] [easy]
P(k)
[tex]2^k<(k+2)![/tex]
[tex]= 2^k < (k+2)(k+1)k![/tex]
P(k+1)
[tex]2^{k+1} < (k+1+2)! [/tex]
[tex]= 2^k \cdot 2 < (k+3)(k+2)(k+1)k![/tex]
its pretty clear that
[tex]2 < k+3[/tex]
how do I show that though
Last edited: