reserve k, m, n, p, K, N for Nat;
reserve i for Integer;
reserve x, y, eps for Real;
reserve seq, seq1, seq2 for Real_Sequence;
reserve sq for FinSequence of REAL;

theorem Th20:
  n>0 & k<=n implies cseq(n).k=((1,1/n) In_Power n).(k+1)
proof
  assume that
A1: n>0 and
A2: k<=n;
  thus ((1,1/n) In_Power n).(k+1) = (n choose k)*(1 ^ (n-k))*((1/n) ^ k) by A2
,Th19
    .= (n choose k)*1*((1/n) ^ k) by POWER:26
    .= (n choose k)*(n ^ (-k)) by A1,POWER:32
    .= cseq(n).k by Def3;
end;
