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

Prove that `sum_(r=0)^n r(n-r)(.^nC_ r)^2=n^2(.^(2n-2)C_n)dot`

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Prove that sum_(r=0)^(2n) r.(""^(2n)C_(r))^(2)= 2n.""^(4n-1)C_(2n-1) .

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If x + y = 1 , prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r) = nx .

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^s C_r=3^n-1.

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prove that sum_(r=0)^n(-1)^r^n C_r . [ 1/(2^r)+(3^r)/(2^(2r))+(7^r)/(2^(3r))+(15^r)/(2^(4r))+ ......up to m terms ] = (2^(m n)-1)/(2^(m n)(2^n-1))

If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Prove that :^(10)C1(x-1)^2-^(10)C2(x-2)^2+^(10)C3(x-3)^2 .....-^(10)C(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Find the sum sum(r=0) .^(n+r)Cr .

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  20. Find the value of (sumsum)(0leiltjlen) (i+j)(""^(n)C(i)+""^(n)C(j)).

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