(C_(1))/(C_(0))+(2*C_(2))/(C_(1))+(3*C_(3))/(C_(2))+...+(20*C_(20))/(C_(19))=

If C_(0), C_(1), C_(2),……, C_(20) are the binomial coefficients in the expansion of (1+x)^(20) , then the value of (C_(1))/(C_(0))+2(C_(2))/(C_(1))+3(C_(3))/(C_(2))+……+19(C_(19))/(C_(18))+20(C_(20))/(C_(19)) is equal to (where C_(r) represetns .^(n)C_(r) )

(""^(20)C_(1))/(""^(20)C_(0))+2.(""^(20)C_(2))/(""^(20)C_(1))+3.(""^(20)C_(3))/(""^(20)C_(2)) +…20.(""^(20)C_(20))/(""^(20)C_(19)) =210

If .^(20)C_(1)+(2^(2)) .^(20)C_(2) + (3^(2)).^(20)C_(3) +......+(20^(2)).^(20)C_(20)=A(2^(beta)) , then the ordered pair (A, beta) is equal to

If .^(20)C_(1)+(2^(2)) .^(20)C_(2) + (3^(2)).^(20)C_(3) +......+(20^(2)).^(20)C_(20)=A(2^(beta)) , then the ordered pair (A, beta) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3)x^(3) + …+ C_(n) x^(n) , then C_(0) - (C_(0) - C_(1)) + (C_(0) + C_(1) + C_(2))- (C_(0) + C_(1) + C_(2)+ C_(3)) + ...+ (-1)^(n-1) (C_0) + C_(1) + C_(2) + ...+ C_(n-1)) , when n is even integer is

Prove that (C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))(C_(n-1)+C_(n))=((n+1)^(n))/(n!)*c_(0)*C_(1)*C_(2).........

Value of r for which expression 20C_(r)^(20)C_(0)+20C_(r-2)^(20)C_(1)+20C_(r-2)^(20)C_(2)+.......+20C_(0)^(20)C_(r) is maximum is equal to (A) 10 (B) 20 (C) 15 (D) 11