I couldn't follow your argument. Instead, start with:
And take this over a common denominator.
Hi all,
I have been given the definition for the binomial coefficient as:
(NOTE: I have written it as (n,k) because I'm not sure how to format it properly using Latex like it is seen in the textbook, with the n above the k. If anyone knows how to do this please let me know).
Now, I am asked to prove that .
Let , then .
Also,
Adding them together gives: .
Now,
So to prove that I need to show:
At this point I know I have done something wrong, because I tried it out with real values (say n=6 and k=3), and they don't match:
Can anyone help?
Thanks in advance
Thanks for that, I managed to solve it using the method you have specified, but I am still not sure why my original method does not work. I have gone over it a few times and still can't see the error in my reasoning. Also, can you tell me where you couldn't follow my working, as hopefully I can clarify/fix it up to make it more understandable.
cheers.