`sumsum_(0leqiltjleq(n-1)) (i.j)C(n,i)C(n,j)` is equal to

sum_(0<=i

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then sumsum_(0lerltslen)(r+s)C_(r)C_(s) is equal to :

Statement 1: sum sum_(0le ilt j le n)(i/ (^n c_i)+j/(^nc_j)) is equal to(n^2)/2a , where a ,sum_(r="0)^(n) 1/(^n"" c_r)="" .="" statement 2:sum_(r=0)^(n) r/(^n" c_r)="sum_(r=0)^(n)(n-r)/(^n" .

The value of (sumsum)_(0leilejlen) (""^(n)C_(i) + ""^(n)C_(j)) is equal to

The value of sum sum_(0<=i<=j<=n)(sim nC_(i)+^(n)C_(j)) is equal to

sum_(0<=i

The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(i-1)) is equal to

(1+x)=C_(0)+C_(1)x+….+C_(n)x^(n) then the value of sumsum_(0lerltslen)C_(r)C_(s) is equal to :

(1+x)=C_(0)+C_(1)x+….+C_(n)x^(n) then the value of sumsum_(0lerltslen)C_(r)C_(s) is equal to :

Find the following sums : (i) sumsum_(inej) ""^(n)C_(i).""^(n)C_(j) , (ii) sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) . (iii) sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) .