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Show that: .^20C13+^20C14-^20C6-^20C7=0...

Show that:` .^20C_13+^20C_14-^20C_6-^20C_7=0`

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Find the value of .^20 C_0-(.^20C_1)/2+(.^20C_2)/3-(.^20C_3)/4+...

The value of "^20 C_0+^(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 a. 2^(19)-(( "^(20)C_10 + "^(20)C_9))/2 b. 2^(19)-((^(20)C 10+2xx^(20)C9))/2 c. 2^(19)-(^(20)C 10)/2 d. none of these

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

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Evaluate the following : (i) 1+.^(20)C_(1)+^(20)C_(2)+^(20)C_(3)+....+^(20)C_(19)+^(20)C_(20) (ii) ^(10)C_(1)+^(10)C_(2)+^(10)C_(3)+.....+^(10)C_(9) (iii)^(25)C_(1)+^(25)C_(3)+^(25)C_(5)+.....+^(25)C_(25) (iv) ^(18)C_(2)+^(18)C_(4)+^(18)C_(4)+^(18)C_(6)+....+^(18)C_(18)

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If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of a^(3) + b^(3) + c^(3) - 3abc is

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