Mathematical induction

• Feb 28th 2012, 08:48 PM
jls7168
Mathematical induction
I am new to mathematical induction and just do not get it at all. I have been working on 5^n < (n+2)! for n>=4 for about 3 hours now. I just do not understand what to do after the k+1 portion of the proof. Any help would GREATLY appreciated.
• Feb 29th 2012, 04:23 AM
FernandoRevilla
Re: Mathematical induction
Quote:

Originally Posted by jls7168
I am new to mathematical induction and just do not get it at all. I have been working on 5^n < (n+2)! for n>=4 for about 3 hours now. I just do not understand what to do after the k+1 portion of the proof. Any help would GREATLY appreciated.

$5^k\leq (k+2)!\Rightarrow 5^{k+1}\leq 5(k+2)!\Rightarrow \;(\textrm{\;as\;}k\geq 4)\;5^{k+1}\leq (k+3)[(k+2)!]=(k+3)!$