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"^10(C0)^2+"^10(C1)^2+"^10(C2)^2+......+...

`"^10(C_0)^2``+``"^10(C_1)^2``+``"^10(C_2)^2``+`......`+`(`"^10C_9)^2``+`(`"^10C_10)^2=`

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^10(C_(0))^(2)-^(10)(C_(1))^(2)+^(10)(C_(2))^(2)-......-(^(10)C_(9))^(2)+(^(10)C_(10))^(2)=

Sum of the series S = 3^(-1)(""^(10)C_(0))-""^(10)C_(1)+(3)(""^(10)C_(2))-3^(2)(""^(10)C_(3))+…+3^(9)(""^(10)C_(10)) is

Prove that 3*""^10C_0+3^2*(""^10C_1)/2+3^3*(""^10C_2)/3+...3^11*(""^10C_10)/11=(4^11-1)/11

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Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9)) .

Prove that ^10C_(1)(x-1)^(2)-^(10)C_(2)(x-2)^(2)+^(10)C_(3)(x-3)^(2)+...-^(10)C_(10)(x-10)^(2)=

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Evaluate : 2^(10)C_(0)+(2^(2).^(10)C_(1))/(2)+(2^(3).^(10)C_(2))/(3)+ . . .+(2^(11).^(10)C_(10))/(11)