Prove that for all positive integers k and n, with k ? n, ? n ? ? k – 1 ? ? k ? = ? k – 1 ? = ? k ? + ???? ? k – 1 ? + ? n – 1 ? ? k – 1 ?
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We need to prove that for all positive integers \( k \) and \( n \), with \( k \leq n \), \[ \binom{n}{k} = \binom{k-1}{k-1} + \binom{k}{k-1} + \cdots + \binom{n-1}{k-1} \] Show more…
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