求证 (14 19:41:33)求证：Ank+kAnk-1=An+1k
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求证(1419:41:33)求证：Ank+kAnk-1=An+1k求证(1419:41:33)求证：Ank+kAnk-1=An+1k求证(1419:41:33)求证：Ank+kAnk-1=An+1k展
求证 (14 19:41:33)求证：Ank+kAnk-1=An+1k
求证 (14 19:41:33)
求证：Ank+kAnk-1=An+1k
求证 (14 19:41:33)求证：Ank+kAnk-1=An+1k
展开：
Ank= (n-0)(n-1)(n-2)*…*(n-k+2)(n-k+1)
kAnk-1= k(n-0)(n-1)(n-2)*…*(n-k+2)
提取(n-0)(n-1)(n-2)*…*(n-k+2)
Ank+kAnk-1=(n-0)(n-1)(n-2)*…*(n-k+2)*（n-k+1+k）
=(n+1)(n-0)(n-1)(n-2)*…*(n-k+2)
=An+1k