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

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

Prove that :^(10)C_1(x-1)^2-^(10)C_2(x-2)^2+^(10)C_3(x-3)^2 .....-^(10)C_(10)(x-10)^2=x^2

The sum (1)/(2)""^(10)C_(0)-""^(10)C_(1)+2.""^(10)C_(2)-2^(2)*""^(10)C_(3)+ . . .+2^(9)*""^(10)C_(10) equals:

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

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

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)=