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# P6 Proof for Binomial Theorem watch

1. This is in the syllabus isn't it?
2. I think so.
3. (Original post by dvs)
I think so.
Would anyone very kindly mind putting a proof up on here (induction)...I was a bit concerned I couldn't do it myself. I'm okay with de Moivre's though!

Cheers.
4. A proof by induction for positive integer binomial powers would be.
5. emm... I can derive the binomial theorem using Maclaurin's series? Is that sufficient?
6. We know that
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
^{n}C_{r}+^{n}C_{r-1}=\frac{n!}{r!(n-r)!}+\frac{n!}{(r-1)!(n-r+1)!}\\

=\frac{n!}{r(r-1)!(n-r)!}+\frac{n!}{(r-1)!(n-r+1)(n-r)!}\\

=\frac{n!(n-r+1)+n!r}{r(r-1)!(n-r)!(n-r+1)}\\

=\frac{(n+1)!}{r!(n-r+1)!\\

=\frac{(n+1)!}{r![(n+1)-r]!}

That is,

We need to use induction to prove:

Assume true for n=k:

For n=k+1:

Thus, if true for n=k then it is also true for n=k+1.
Clearly it is true for n=1 as: and by the binomial theorem

Hence it is true for n=1,1+1=2,2+1=3.... and so on for all positive integral n.
7. (Original post by hello)
Would anyone very kindly mind putting a proof up on here (induction)...I was a bit concerned I couldn't do it myself. I'm okay with de Moivre's though!

Cheers.
some notes and a proof attached
Attached Images
8. binomial.pdf (99.8 KB, 124 views)
9. Cheers guys. On top form as usual!

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