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[obm-l] COMBINATORIA - Putnam 87
- To: obm-l@xxxxxxxxxxxxxx
- Subject: [obm-l] COMBINATORIA - Putnam 87
- From: Joÿffffe3o Silva <d79i3mn8@xxxxxxxxxxxx>
- Date: Wed, 24 Jan 2007 18:44:04 +0000 (GMT)
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Sejam r, s, t inteiros não-negativos com r + s <= t. Prove que
C(s,0)/C(t,r) + C(s,1)/C(t,r+1) + C(s,2)/C(t,r+2) + ... + C(s,s)/C(t,r+s) =
= (t+1)/((t+1-s) C(t-s,r)), onde C(n,k) = [n(n-1)...(n+1-k)]/[k(k-1)...3*2*1]
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