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# Induction watch

1. Proof by induction:

I'm stuck on the inductive step, the factorials are really messing me up. Could anyone link me to a video which will help me understand how to do these summation proofs with factorials or perhaps explain how I go about solving this?

The form I need somehow get this in is:
2. (Original post by FamilyFirst)
Proof by induction:

I'm stuck on the inductive step, the factorials are really messing me up. Could anyone link me to a video which will help me understand how to do these summation proofs with factorials or perhaps explain how I go about solving this?

The form I need somehow get this in is:
Pull out a common factor of (k+1)!:

(k+1)! - 1 + (k+1)(k+1)! = (k+1)!(1 + k + 1) - 1 = (k+2)(k+1)! - 1

But you know that k! = k * (k-1) * (k-2) * ... * 1 = k(k-1)! = k(k-1)(k-2)! stc...

So it makes sense that (k+2)! = (k+2)(k+1)(k)(k-1)...(1) = (k+2)(k+1)!

So your simplification of (k+2)(k+1)! - 1 becomes...?

Oh, andsorry for no LaTeX - I'm half aslee and on my phone.
3. (Original post by Zacken)
...
What becomes of (k + 1)! when you multiply it with 1 & k
4. (Original post by FamilyFirst)
What becomes of (k + 1)! when you multiply it with 1 & k
1 + k + 1 = k + 2
5. (Original post by Zacken)
1 + k + 1 = k + 2
I still don't understand why you did that though :?
6. (Original post by FamilyFirst)

The form I need somehow get this in is:
Okay, I'm on my computer so I can explain this a bit more in depth now. We have: now we can pull out a common factor of , if you cannot see this, let us call so that we have:

then pulling out the common factor of from the first two terms, we have: .

Replacing by and remembering that we have: .

But so we can say that:

7. (Original post by Zacken)
But
Yeah that was very smart. I don't think a dopey dude like me would realise that in the instant. Do you think something like this would come up in Edexcel?

I understood everything you did, but do you know where I can get some extra practice on this, as I don't feel very confident with it?
8. (Original post by FamilyFirst)
Yeah that was very smart. I don't think a dopey dude like me would realise that in the instant. Do you think something like this would come up in Edexcel?

I understood everything you did, but do you know where I can get some extra practice on this, as I don't feel very confident with it?
Aye, this is something that comes with practice - once you see how it's done, you should keep an eye out on it all the time. I'm farily certain it can, has and could/would come up on Edexcel.

The last two pages on this look good.
9. (Original post by Zacken)
Aye, this is something that comes with practice - once you see how it's done, you should keep an eye out on it all the time. I'm farily certain it can, has and could/would come up on Edexcel.

The last two pages on this look good.
Great,

thanks!
10. (Original post by FamilyFirst)
Great,

thanks!
Quote me if you need any help on those problems.

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