I saw the formula of negative binomial expression here Here I know that in common notion is that the numbers in large bracket just after sign of summation represents combination of below w.r.t to above.Here can you tell me how do we involve negative number in combination & do (-n)Ck.Means how can we find combination of negative number (-n) here
2026-02-23 10:00:57.1771840857
Combination of negative term in negative Binomial expression.
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If $n$ and $k$ are positive integers with $k\le n$ then the formula $${n\choose k}={n(n-1)(n-2)\cdots(n-k+1)\over k!}$$ has a combinatorial interpretation as the number of ways of choosing $k$ things from $n$ things. When $n$ is not a positive integer with $k\le n$, the formula no longer has that combinatorial interpretation, but it still indicates a legal computation, and is taken to be the definition of $n\choose k$. And even though it doesn't have that combinatorial interpretation, it still has many uses in combinatorics and elsewhere (to begin with, in the general form of the Binomial Theorem).