Subtraction of combinations

Asked Jul 30 '17 at 13:37

Active Jul 30 '17 at 13:56

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I'm aware of the Pascal's Identity which we use it for solving question but I'm looking for an identity for substracting combinations . For example how we can rewrite $C(n, k+1) - C(n , k)$?

Note : Honestly , I was solving a problem and then I get to this .

edited Jul 30 '17 at 13:56

asked Jul 30 '17 at 13:37

S.H.W

4,379

what was the problem ? what has been tried? I could actually use this math in some of my attempted Lucas-Lehmer test questions for example. the first is how many times the second ? – Jul 30 '17 at 13:41
@RoddyMacPhee It's the problem : $C(n,4) = 14 + C(n,3)$ Now find $\frac{n(n-1)}{2}$. – S.H.W Jul 30 '17 at 13:44
again I'll tell you find there ratio first. – Jul 30 '17 at 13:47
Can you explain more ? – S.H.W Jul 30 '17 at 13:49
what is the formula for n choose k. – Jul 30 '17 at 13:50
$\frac{n!}{(n-k)!k!}$ – S.H.W Jul 30 '17 at 13:51
Let us continue this discussion in chat. – Jul 30 '17 at 13:51

Subtraction of combinations

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