Home
Class 11
MATHS
Prove that ^10 C1(x-1)^2-^(10)C2(x-2)^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`

Promotional Banner

Similar Questions

Explore conceptually related problems

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)=

Prove that ""^(10)C_(2)+2xx^(10)C_(3)+^(10)C_(4)=^(12)C_(4)

Let X=(^(10)C_(1))^(2)+2(^(10)C_(2))^(2)+3(^(10)C_(3))^(2)+...+10(^(10)C_(10))^(2) where ^(10)C_(r),r in{1,2,;10} denote binomial coefficients.Then,the value of (1)/(1430)X is

Let X=(\ ^(10)C_1)^2+2(\ ^(10)C_2)^2+3(\ ^(10)C_3)^2+\ ddot\ +10(\ ^(10)C_(10))^2 , where \ ^(10)C_r , r in {1,\ 2,\ ddot,\ 10} denote binomial coefficients. Then, the value of 1/(1430)\ X is _________.

Let X=(\ ^(10)C_1)^2+2(\ ^(10)C_2)^2+3(\ ^(10)C_3)^2+\ ddot\ +10(\ ^(10)C_(10))^2 , where \ ^(10)C_r , r in {1,\ 2,\ ddot,\ 10} denote binomial coefficients. Then, the value of 1/(1430)\ X is _________.

Let X=(\ ^(10)C_1)^2+2(\ ^(10)C_2)^2+3(\ ^(10)C_3)^2+\ ddot\ +10(\ ^(10)C_(10))^2 , where \ ^(10)C_r , r in {1,\ 2,\ ddot,\ 10} denote binomial coefficients. Then, the value of 1/(1430)\ X is _________.

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

4(10/x)^2-6(10/x)^2+3(10/x)^2=1