Find the value of `underset(0leiltjlen)(sumsum)(.^(n)C_(i)+.^(n)C_(j))`.

Find the value of (sumsum)_(0leiltjlen) (1+j)(""^(n)C_(i)+""^(n)C_(j)) .

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following underset(0leile jlen)(sumsum)C_(i)C_(j)

Find the value of sumsum_(0leiltjlen) (""^(n)C_(i)+""^(n)C_(j)) .

For any n in N, let C_(r) stand for ""^(n)C_(r) , r = 0,1,2,3,…,n and let S= sum_(r=0)^(n) (1)/(C_(r)) Statement-1: underset(0leilt i le n)(sumsum) ((i)/(C_(i))+(j)/(C_(j)))= (n^(2))/(2)S Statement-2: underset(0leilt i le n)(sumsum) ((1)/(C_(i))+(1)/(C_(j)))= nS

Find the value of sumsum_(0leilejlt=n)(i+j)(nC_i+n C_j)dot

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

Find the sum sumsum_(0leiltjlen)"^nC_i

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

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

Find the value of n: (i) .^(n)C_(10)=^(n)C_(16) (ii) .^(15)C_(n) =^(15)C_(n+3) (iii) .^(10)C_(n) =^(10)C_(n+2) (iv) .^(25)C_(3n) =.^(25)C_(n+1) (v) .^(n)C_(r) =.^(n)C_(r-2)