Question

Could someone please explain to me how this got summed?

Answer 1

\[\sum_{i=0}^k \binom ni \binom n{k-i}=\binom {n+n}k\]

Answer 2

I can see that they're just adding the values, but I've been trying to find the pattern over the series for a few hours and don't see it.

Answer 3

@wio

Answer 4

Hmmm. At first I think of binomial theorem, but it doesn't quite match it.

Answer 5

I'm thinking of something like this:\[
(x+y)^n = \sum_{k=0}^{n}{n\choose k}x^ky^{n-k}
\]

Answer 6

To the \(n\)th power is permutations replacement

Answer 7

hmm I see what you mean. I'll explore that version in a bit - this was just out of my own curiosity. I'm actually somewhat stuck on this final problem, just tedious and I've had a long day, could you just watch over my work to make sure I don't make any mistakes please?

Answer 8

I can watch.