# Mathematical Induction

• May 29th 2013, 10:26 AM
mcolula
Mathematical Induction
Hi, i have been reading a mathematical indcution book and i start answering the exercises but i think i have a problem with this one, I'll be grateful if you help

# Problem
Determine Un if we know that U1=1 and Uk=Uk-1 + 3. for K>1.
suggestion: U1=3*1 - 2, U2=3*2 - 2
• May 29th 2013, 10:39 AM
HallsofIvy
Re: Mathematical Induction
Quote:

Originally Posted by mcolula
Hi, i have been reading a mathematical indcution book and i start answering the exercises but i think i have a problem with this one, I'll be grateful if you help

# Problem
Determine Un if we know that U1=1 and Uk=Uk-1 + 3. for K>1.
suggestion: U1=3*1 - 2, U2=3*2 - 2

In other words, they "suggest" that the general formula is Un= 3n- 2[/sub].
All you need to do is show that this does, in fact, satisfy the recursion.
If Un= 3n- 2, then Uk-1= 3(k- 1)- 2= 3k- 5, Uk= 3k- 2 and it is certainly true that Uk= 3k- 2= 3k- 5+ 3= U[sub]k-1]+ 3
• May 29th 2013, 07:37 PM
ibdutt
Re: Mathematical Induction
• May 30th 2013, 09:02 AM
mcolula
Re: Mathematical Induction
I found the solution to this problem on my book, i just need one more thing, the solution on the book is:

1° - the hypothesis is valid for N=1
2° - with Uk = 3k-2

then

Uk+1 = Uk + 3 = 3k - 2 + 3 = 3(k+1) - 2 //This is the solution

I just want someone explain me why Uk+1 is equal to Uk + 3 especially why that three.