Induction Help (1 Viewer)

alussovsky

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So I came across this induction question and am quite stuck mid-way.
The question is: Prove that is divisible by for all odd integers

So far, I have this working out done:

1. To prove: , where
Prove true for

which is divisible by 3
So the statement is true for

2. Assume true for , where
i.e. , where

3. Prove true for
To prove: , where


Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!
 

InteGrand

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So I came across this induction question and am quite stuck mid-way.
The question is: Prove that is divisible by for all odd integers

So far, I have this working out done:

1. To prove: , where
Prove true for

which is divisible by 3
So the statement is true for

2. Assume true for , where
i.e. , where

3. Prove true for
To prove: , where


Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!
 

HeroWise

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So I came across this induction question and am quite stuck mid-way.
The question is: Prove that is divisible by for all odd integers

So far, I have this working out done:

1. To prove: , where
Prove true for

which is divisible by 3
So the statement is true for

2. Assume true for , where
i.e. , where

3. Prove true for
To prove: , where


Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!
some critisicm: when you say always say or since by only you can include the negative set which is Wrong. Since Induction USUALLY deals with


Anyway, for step 2, the assumption satge I would say and for the proving step, I would let ; it makes it easier this way!
 

alussovsky

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Thank you for pointing that out! Even in written down working out, I keep forgetting that plus sign, so I'll make sure to check that it's in next time, haha.

In class, my teacher said that when proving for odd integers, you should always use the assumption so that the odd integer 1 is not excluded! Is that true or is still alright to use ?
 

InteGrand

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Thank you for pointing that out! Even in written down working out, I keep forgetting that plus sign, so I'll make sure to check that it's in next time, haha.

In class, my teacher said that when proving for odd integers, you should always use the assumption so that the odd integer 1 is not excluded! Is that true or is still alright to use ?
 

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