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(C(0)+C(1))(C(1)+C(2))(C(2)+C(3))...(C(n...

`(C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))...(C_(n-1)+C_(n))=(C_(0).C_(1).C_(2)......C_(n-1)(n+1)^(n))/(n!)`.

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(C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))(C_(3)+C_(4)).........(C_(n-1)+C_(n))=(C_(0)C_(1)C_(2).....C_(n-1)(n+1)^(n))/(n!)

Prove that (C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))(C_(n-1)+C_(n))=((n+1)^(n))/(n!)*c_(0)*C_(1)*C_(2).........

(C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+.........(C_(n))/(n+1)=

(C_(1))/(C_(0))+2(C_(2))/(C_(1))+3(C_(3))/(C_(2))+.........+n(C_(n))/(C_(n-1))=(n(n+1))/(2)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3)x^(3) + …+ C_(n) x^(n) , then C_(0) - (C_(0) - C_(1)) + (C_(0) + C_(1) + C_(2))- (C_(0) + C_(1) + C_(2)+ C_(3)) + ...+ (-1)^(n-1) (C_0) + C_(1) + C_(2) + ...+ C_(n-1)) , when n is even integer is

If quad (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n), then C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+...+C_(n-2)C_(n)=((2n)!)/((n!)^(2)) b.((2n)!)/((n-1)!(n+1)!) c.((2n)!)/((n-2)!(n+2)!) d.none of these

MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. Prove that : .^(n-1)C(r)+.^(n-2)C(r)+.^(n-3)C(r)+.........+.^(r)C(r)...

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  2. Given s = 1 + q + q^2+. . . . + q^n, Sn = 1 +(q+1 /2)+(q+1 /2)^2+........

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  3. (C(0)+C(1))(C(1)+C(2))(C(2)+C(3))...(C(n-1)+C(n))=(C(0).C(1).C(2)........

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  4. If P(n) denotes the product of all the coefficients in the expansion o...

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  5. Prove that (i) C(1)+2C(2)+3C(3)+……+nC(n)=n.2^(n+1) (ii) C(0)+(C(1)...

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  6. 2.C(0)+(2^(2).C(1))/(2)+(2^(3).C(2))/(3)+(2^(4).C(3))/(4)+......+(2^(n...

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

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  8. (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + C(3) x^(3) + … + C(n) x^(n)...

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

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

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

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

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

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

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

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

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

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

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  19. 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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  20. 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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