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If (1 + x)^(n) = C(0) = C(1) x + C(2) x...

If ` (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)` ,
find the values of the following
`underset(0leile jlen)(sumsum)C_(i)C_(j) `

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MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + C(3) x^(3) + … + C(n) x^(n)...

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  2. prove that : C0^2+3C1^@+5C2^2+...+(2n+1)Cn^2=((n+1)2n!)/(n!)^2

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  3. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

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  4. Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...+sqrt(Cn)le 2^(n-1) +(n-1)/...

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  5. If C(r ) = (n!)/(r!(n - r)!), then prove that sqrt(C(1)) + sqrt(C(2)...

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  6. Sum of all the digits of the coefficient of x^(5) in the expansion of ...

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  7. Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...

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  8. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

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  9. Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...

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  10. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

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  11. Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...

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  12. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

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  13. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

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  14. If n(j(r))=((1-xn)(1-x(n-1))(1-x^(n-2)).......(1-x^(n-r+1)))/((1-x)(1-...

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  15. Prove that sum(k=0)^n ^nCk sinKx.cos(n-K)x=2^(n-1)sin nx

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  16. The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+.............

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  17. Find the coefficients of x^(6) in the expansion of (ax^(2) + bx +...

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  18. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax-by+cz)^9

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  19. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cx...

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  20. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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