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If .^(20)C(1)+(2^(2)) .^(20)C(2) + (3^(2...

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

A

(420, 19)

B

(420, 18)

C

(380, 18)

D

(380, 19)

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The correct Answer is:
B
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The value of 1^(1).^(20)C_(1)+2^(2).^(20)C_(2)+3^(2).^(20)C_(3)+….+(20)^(2).^(20)C_(20) is

1.^(20)C_(1)-2.^(20)C_(2)+3.^(20)C_(3)-...-20.^(20)C_(20)

The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

The sum of the series 20C_(0)-^(20)C_(1)+^(20)C_(2)-^(20)C_(3)+...-...+^(20)C_(10) is:

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

The value of .^(20)C_(10)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_(4)+.^(20)C_(12)+.^(20)C_(13)+.^(20)C_(14)+.^(20)C_(15) is

if 3^(1)20C_(0)+(3^(2))/(2)20C_(1)+(3^(3))/(3)20C_(2)+............ upto 21 terms =(2^(a)-1)/(b) then the the value of (b)/(a) equal to :

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