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# FP1 Proof by induction help watch

1. I'm stuck on the following question:

Prove by induction that for all

I've done the n=1 step, which is true as both come out as -2

I then replaced n with k and assume it to be true.

I then put in k+1 in with the (k+1)th term being however I'm not sure if it is right. If it is then I can't do the algebra proving that this is equal to the original statement with k+1

2. Do you mean and not ?
3. (Original post by heymynameisben)
I'm stuck on the following question:

Prove by induction that for all

I've done the n=1 step, which is true as both come out as -2

I then replaced n with k and assume it to be true.

I then put in k+1 in with the (k+1)th term being however I'm not sure if it is right. If it is then I can't do the algebra proving that this is equal to the original statement with k+1

I haven't looked at where you got that from you in detail but you should follow this kind of structure: (after the basis case obviously which you've done)

And by assuming that is true then

Do you know where to go from there:
4. (Original post by dr_98_98)
Do you mean and not ?
Yes I did, my mistake
5. (Original post by ElMoro)
I haven't looked at where you got that from you in detail but you should follow this kind of structure: (after the basis case obviously which you've done)

And by assuming that is true then

Do you know where to go from there:
That's the stage I got to but I'm afraid I'm not totally sure when to go from there.
Do you try and prove it's equal to ?
If that's right then I'm having difficulties rearranging to equal each other. Thanks
6. (Original post by heymynameisben)
That's the stage I got to but I'm afraid I'm not totally sure when to go from there.
Do you try and prove it's equal to ?
If that's right then I'm having difficulties rearranging to equal each other. Thanks
Can you post your working? Hint: factor theorem.
7. (Original post by ElMoro)
Can you post your working? Hint: factor theorem.
Boom, just got it. Thanks for your help
8. (Original post by heymynameisben)
Boom, just got it. Thanks for your help
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