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 U_{n} if we know that U_{1}=1 and U_{k}=U_{k-1 }+ 3. for K>1.

suggestion: U_{1}=3*1 - 2, U_{2}=3*2 - 2

In other words, they "suggest" that the general formula is U_{n}= 3n- 2[/sub].

All you need to do is show that this does, in fact, satisfy the recursion.

If U_{n}= 3n- 2, then U_{k-1}= 3(k- 1)- 2= 3k- 5, U_{k}= 3k- 2 and it is certainly true that U_{k}= 3k- 2= 3k- 5+ 3= U[sub]k-1]+ 3

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Re: Mathematical Induction

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 U_{k} = 3k-2

then

U_{k+1} = U_{k} + 3 = 3k - 2 + 3 = 3(k+1) - 2 //This is the solution

I just want someone explain me why U_{k+1} is equal to U_{k} + 3 **especially** why that three.

thanks for your help.

Re: Mathematical Induction

It is what you have been given in the question.

Determine Un if we know that U1=1 and Uk=Uk-1 + 3. for K>1.

just replace k by k+1