Induction help!!! (1 Viewer)

[kangarulz]

ahh i can't remember how to do the proving step in induction for n=k+1

i just can't remember how i'm suppose to sub it in then prove it so its the right answer at the end

 

[airie]

You need to deduce that the statement to be proven holds true for k+1, if it is known that it holds for a number k. What is the question?

 

[kangarulz]

i've worked it out now for the summation problems, i'm just strugglign with the divisibility ones now

 

[SoulSearcher]

As soon as you can assume it, use the assumption n=k and then manipulate the terms until you get it to the form where n = k+1.

 

[Riviet]

i've worked it out now for the summation problems, i'm just strugglign with the divisibility ones now

What's your method for the divisibility ones?

 

[pLuvia]

This one is too easy to be an exam question, but this is gist of proving the divisible ones

For example for proving that 9ⁿ is divisble by 3 for postiive n, by mathematical induction

Show true for n=1
S(1)=9
Which is divisble by 3

Assume n=k
S(k)=9^k=3N (where N is an integer)
Let n=k+1
S(k+1)=9^k+1
=9^k.9
=3N.9 [From assumption]

Therefore it is divisible by 3. Hence if n=k is true, then n=k+1 is true, then by mathematical induction the statement is divisible by 3 for all positive n

 

[acmilan]

^^do you mean if n=k is true than n=k+1 is true?

 

[pLuvia]

^^do you mean if n=k is true than n=k+1 is true?

Yeh that