" The arithmetic mean of the series "^(n)C_(0),^(n)C_(1),^(n)C_(2)...^(n)C_(n)" is "

The arithmetic mean of ""^(n)C_(0),""^(n)C_(1),""^(n)C_(2), ..., ""^(n)C_(n) , is

The arithmetic mean of ""^(n)C_(0),""^(n)C_(1),""^(n)C_(2), ..., ""^(n)C_(n) , is

The arithmetic mean of ""^(n)C_(0), ""^(n)C_(1), ""^(n)C_(2)…., ""^(n)C_(n) is

The A.M. of the series .^(n)C_(0), .^(n)C_(1), .^(n)C_(2),….,.^(n)C_(n) is

The A.M. of the series .^(n)C_(0), .^(n)C_(1), .^(n)C_(2),….,.^(n)C_(n) is

The mean of then Numbers 0,1,2,3.......n with respective weights ""^(n)C_(0),""^(n)C_(1),""^(n)C_(2)........""^(n)C_(n) is

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

If n in N then hat sim(n)C_(0)+^(n+1)C_(1)+^(n+2)C_(2)+....+^(n+r)C_(i) is equal to