$ \sum_{k=r}^{n} {n \choose k} = \sum_{k = r - 1}^{n-1}{k \choose r -1}2^{n-1-k} $
The proof is trivial but I haven't seen this identity anywhere. Perhaps it's a special case of a more general identity?
$ \sum_{k=r}^{n} {n \choose k} = \sum_{k = r - 1}^{n-1}{k \choose r -1}2^{n-1-k} $
The proof is trivial but I haven't seen this identity anywhere. Perhaps it's a special case of a more general identity?