Prove, algebraically and logically, that the combination equation:
nCr + nC(r+1) = (n+1)C(r+1)

Question

Prove, algebraically and logically, that the combination equation:
nCr + nC(r+1) = (n+1)C(r+1)

anonymous · Answer

$$\left(\begin{matrix}n \ r\end{matrix}\right) + \left(\begin{matrix}n \ r+1\end{matrix}\right) = \left(\begin{matrix}n+1 \ r+1\end{matrix}\right)$$

anonymous · Answer

Do you mean algebraic and combinatorial?

anonymous · Answer

Just without the use of number substitutions.

anonymous · Answer

Why don't you just expand it and see ...

anonymous · Answer

How are you meant to expand it. My teacher showed me very quickly today then rubbed it out, all I remember is it started by changing it to factorial form.

anonymous · Answer

$ \huge \binom{n}{r} = \frac{n!}{r!\times(n-r)!} $