Ramus's Identity/Examples
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Examples of Ramus's Identity
Example: $k = 1, m = 3$
| \(\ds \sum_{j \mathop \ge 0} \binom n {3 j + 1}\) | \(=\) | \(\ds \binom n 1 + \binom n 4 + \binom n 7 + \cdots\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 3 \paren {2^n + 2 \cos \frac {\paren {n - 2} \pi} 3}\) |