# help in number theory (mathematical induction)

• May 6th 2012, 11:59 PM
stelakos
help in number theory (mathematical induction)
Hallo i introduced my self tou your forum and i would like you to help me in problems such are mathematical induction inequalities.i mean i can solve simple equalities cause i can just replace using previous equalities and finnaly prove what i need to prove.my problem is that i dont know what to do in even simple to solve inequalities like ""prove that 5^n>5v-1 n belongs to N*...english is not my primary language and i cannot use it as i would like to so if you dont understand anything please feel free to ask ;) its my first post so it may have several things that need further explanation i would be glad explaining them and at last have my issue solved :D
• May 7th 2012, 08:51 AM
HallsofIvy
Re: help in number theory (mathematical induction)
First, your English is far better than my (put pretty much any language here)! But your equation may be wrong: 5^n> 5v- 1 doesn't make sense. Did you mean 5^n> 5n-1?

To prove that using "mathematical induction" you do two things- first verify the statement for n= 1: 5^1= 5> 4= 5(1)- 1. So that's true.

Now prove "if the statement is true for n= k, it is also true for n= k+1.
If 5^k> 5k- 1, and 5> 0, 5^{k+1}> 5(5^k)> 5(5k-1). Now you need to prove that that, 5(5k- 1)= 25k- 5, is greater than or equal to 5(k+1)- 1= 5k- 4.
• May 7th 2012, 12:23 PM
stelakos
Re: help in number theory (mathematical induction)
thanks a lot m8 :) and yes i meant 5^n>5n-1.i understand everything till the point you start that thing,"" 5^{k+1}> 5(5^k)> 5(5k-1). Now you need to prove that that, 5(5k- 1)= 25k- 5, is greater than or equal to 5(k+1)- 1= 5k- 4.""i mean how do you get that ""5^{k+1}> 5(5^k)> 5(5k-1)"" and that part "" is greater than or equal to 5(k+1)- 1= 5k- 4"" i would be glad if you explain them more... i know im a bit newbie at maths so i dont get new things quicly