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Prove that :^(10)C1(x-1)^2-^(10)C2(x-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`

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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 _________.

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)) .

The value of (.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10)) is

Find the sum 2..^(10)C_(0) + (2^(2))/(2).^(10)C_(1) + (2^(3))/(3).^(10)C_(2)+(2^(4))/(4).^(10)C_(3)+"...."+(2^(11))/(11).^(10)C_(10) .

"^(30)C_(0)*^(20)C_(10)+^(31)C_(1)*^(19)C_(10)+^(32)C_(2)*18C_(10)+....^(40)C_(10)*^(10)C_(10) is equal to

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((2n-1)!)/([(n-1)!]^(2))

Find value of the series .^(10)C_1+^(10)C_2+...+^(10)C_9dot

The sum of series .^(20)C_0-^(20)C_1+^(20)C_2-^(20)C_3++^(20)C_10 is 1/2 .^(20)C_10 b. 0 c. .^(20)C_10 d. -^(20)C_10

If underset(xrarroo)"lim"((1+x)^(10)+(x+2)^(10)+....+(x+100)^(10))/(x^(10)+10^(10)) =K^(2) , then the value of K will be -

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1))=(n(n-1))/(2)

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the cube root of 27

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  2. Find the coefficient of x^2 in (a/(a+x))^(1//2)+(a/(a-x))^(1//2)

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  3. Prove that :^(10)C1(x-1)^2-^(10)C2(x-2)^2+^(10)C3(x-3)^2 .....-^(10)C(...

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  4. If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the...

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  5. Prove that sum(r=0)^n r(n-r)(.^nC r)^2=n^2(.^(2n-2)Cn)dot

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  6. Prove that 1-^n C1(1+x)/(1+n x)+^n C2(1+2x)/((1+n x)^2)-^n C3(1+3x)/((...

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  7. Find the coefficient of x^(20) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

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  8. The number of terms in the expansion of (a+b+c)^n where ninN is

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  9. Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x...

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  10. Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

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  11. Find the coefficient of x^k in1+(1+x)+(1+x)^2++(1+x)^n(0lt=klt=n)dot

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  12. The term independent of x in the expansion of (1+x+2x^3)(3/2(x^2)-1/(3...

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  13. If aa n db are distinct integers, prove that a-b is a factor of a^n-b^...

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  14. Find a, b and n in the expansion of (a+b)^(n) if the first three term...

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  15. Find the coefficient of x^(25) in expansion of expression sum(r=0)^(50...

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  16. If the sum of the coefficients of the first, second, and third terms ...

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  17. If p+q=1, then show that sum(r=0)^nr^2^nCrp^rq^(n-r)=npq+n^2p^2

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  18. If every pair from among the equations x^2+a x+b c=0. x^2+b x+c a=0,a ...

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  19. Prove that ^mC1^n Cm-^m C2^(2n)Cm+^m C3^(3n)Cm-.....=(-1)^(m-1)n^mdot

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  20. Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn +^nC2 ^(2n-4)Cn =2^n

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